Research ArticleCandidates for Synergies Linear Discriminants versusPrincipal Components

Ramana Vinjamuri1 Vrajeshri Patel1 Michael Powell2

Zhi-Hong Mao3 and Nathan Crone4

1 Department of Biomedical Engineering Stevens Institute of Technology Hoboken NJ 07030 USA2Department of Biomedical Engineering Johns Hopkins University Baltimore MD 21205 USA3Department of Electrical and Computer Engineering and the Department of BioengineeringUniversity of Pittsburgh Pittsburgh PA 15261 USA

4Department of Neurology and Neurological Surgery Johns Hopkins UniversityBaltimore MD 21287 USA

Correspondence should be addressed to Ramana Vinjamuri ramanavinjamuristevensedu

Received 3 March 2014 Revised 5 July 2014 Accepted 5 July 2014 Published 17 July 2014

Academic Editor Fabio Babiloni

Copyright copy 2014 Ramana Vinjamuri et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Movement primitives or synergies have been extracted from human hand movements using several matrix factorizationdimensionality reduction and classification methods Principal component analysis (PCA) is widely used to obtain the first fewsignificant eigenvectors of covariance that explain most of the variance of the data Linear discriminant analysis (LDA) is also usedas a supervised learning method to classify the hand postures corresponding to the objects grasped Synergies obtained using PCAare principal component vectors aligned with dominant variances On the other hand synergies obtained using LDA are lineardiscriminant vectors that separate the groups of variances In this paper time varying kinematic synergies in the human handgrasping movements were extracted using these two diametrically opposite methods and were evaluated in reconstructing naturaland American sign language (ASL) postural movements We used an unsupervised LDA (ULDA) to extract linear discriminantsThe results suggest that PCA outperformed LDA The uniqueness advantages and disadvantages of each of these methods inrepresenting high-dimensional hand movements in reduced dimensions were discussed

1 Introduction

The central nervous system (CNS) is responsible for gen-erating a potentially infinite set of hand postures used ineveryday tasks such as grasping objects It is hypothesized thatthe CNS reduces this computational burden by combining adiscrete set of movement primitives or synergies [1 2] Thisallows high degree-of-freedom (DoF) control using a lowerdimensional subspace [3] Ninety percent of natural graspmovements produced by the human hand which has greaterthan 25 DoF [4] have been reconstructed using five or sixsynergies [5 6] For these reasons synergies have potentialapplications in dexterous control of prosthetic hands andhave been recently applied to brain machine interfaces used

in neural prosthesis [3 7 8] However deriving these syn-ergies to effectively represent and reconstruct human handmovements poses a challenge To address this challenge sev-eral linear and nonlinear dimensionality reduction methodshave been explored

Nonlinear dimensionality reduction methods aim toreduce high-dimensional nonlinear data to a lower dimen-sional manifold Gaussian process latent variable model[9] geodesic trajectory generation models [10] Isomap [11]gradient descent method [12] and radial basis function [8]have been used to decompose upper limb movements eitherin kinematic ormuscle space Similarly linear dimensionalityreduction methods aim to transform a high-dimensionalspace to a linear low-dimensional subspace Particularly

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2014 Article ID 373957 10 pageshttpdxdoiorg1011552014373957

2 Computational Intelligence and Neuroscience

successful in natural datasets linear dimensionality reduc-tion methods include nonnegative matrix factorization(NMF) principal component analysis (PCA) and lineardiscriminant analysis (LDA) Ajiboye and Weir [13] usedNMF on mimed American sign language (ASL) postures todetermine muscle synergies and found that subject-specificsynergies were characterized by coactivation of muscleswhile population (similar across all subjects) synergies weretypically dominated by a single muscle PCA has been widelyused to extract postural kinematic and muscle synergies[6 14ndash17] Mason et al [14] used PCA implemented withsingular value decomposition on a set of grasping tasksand found that the first eigenposture resembled a wholehand grasp This is similar to the results by [5 14 15]Tresch et al [18] compared multiple matrix factorizationalgorithms including PCA independent component analysis(ICA) NMF factor analysis (FA) and combinations of theabove to determine muscles synergies He found that thebest performing methods (FA ICA NMF ICAPCA andprobabilistic ICA) identified similar synergies Dimensional-ity reduction methods not only yield significant eigenvectorsfromphysiological data but also reflect patterns inmovementgeneration Hence two contrasting dimensionality reductionmethods such as PCA and LDA may be partial towards dif-ferent kinematic movement primitives By comparing thesetwo methods we can determine which kinematic propertiesare most important in movement generation

PCA attempts to accurately represent the data in low-dimensional space by projecting the data in the directions ofmaximum variance as shown in Figure 1(a) PCA performedon a sample dataset is shown hereThe first principal compo-nent axis corresponds to the direction of maximum varianceof the data and similarly second and third in the decreasingorder LDA was used to classify the same sample dataset(Figure 1(b)) Directions of maximum variance as seen inPCA are not useful for classification Hence LDA projectsthe data in directions that preserve maximum separationor discrimination in groups or classes of data LDA seeksdimensionality reduction while preserving as much classdiscrimination as possible

In this paper we compared two contrasting methodsPCA and LDA in deriving synergies and evaluated themon a set of natural grasping and ASL postural movementsBoth PCA and LDA are linear dimensionality reductionmethods that reduce high-dimensional movements of thehand by looking for either most common patterns (PCA) ordistinct separable patterns (LDA) While previous researchhas identified a limited number of discriminatingmuscles in asingle synergy such patterns have not been seen in kinematicspace As LDA aims to separate data resulting synergies mayreflect distinct patterns Although LDA is a type of clusteringmethod it offers a direct contrast to PCA separating variance(LDA) ormaximizing variance (PCA)Thus we can interpretthe strengths and weaknesses of both methods In orderto maintain fairness in comparison with PCA which is anunsupervised method LDA used in this paper was alsounsupervised (ULDA) first by labeling the data with k-meansclustering and then classifying it using classical LDA

2 Methods

21 Materials and Experiment In the experiment we used aCyberGlove (CyberGlove Systems LLC San Jose CA USA)equipped with 22 sensors that captured hand movementsat a sampling frequency of 86Hz In this paper we onlyconsidered 10 of the sensors which measure the angles of thecarpometacarpal (CMC)metacarpophalangeal (MCP) jointsof the thumb and the MCP and proximal interphalangeal(PIP) joints of the other four fingers These 10 joints cancapture most characteristics of the hand in grasping tasksWe used several objects of different shapes (spheres circulardiscs rectangles pentagons nuts and bolts) and differentdimensions (spheres 1ndash5 cm in radius discs 2ndash10 cm inradius rectangles and pentagons 1ndash3 cm each side nuts andbolts 2ndash5 cm in length) in the grasping tasks 10 subjectsparticipated in this experiment after signing the consentforms approved by the Institutional Review Board (IRB) ofthe University of Pittsburgh

A typical task consisted of grasping the above objectsStart and stop times of each task were signaled by computer-generated beeps In each task the subject was in a seatedposition resting hisher right hand at a corner of a table andupon hearing the beep and grasped the object placed onthe table At the time of the start beep the hand was in restposture and then the subject grasped the object and held ituntil the stop beep

In the first phase subjects were instructed to rapidly grasp50 objects one at a time This was repeated for the same 50objects and thus the whole training phase obtained 100 rapidgrasps Rapid grasping movements from the first phase wereused in deriving synergies We assume that by minimizingreaction time and minimizing continuous sensory feedbackthe resulting task space is driven by synchronous weightedsynergies resulting from impulses originating in a higherlevel of neural system The rapid movement is achieved asa weighted sum of synchronous synergies Only these 100rapid grasps were used in extracting synergies using PCA andULDA

In the second phase subjects were instructed to graspthe above 50 objects naturally (slower than the rapid grasps)and then this was repeated So far the tasks involved onlygrasping In the third phase to test the generalizability ofthe synergies over a broad range of postures subjects werealso asked to imitate 36 (10 numbers and 26 alphabet letters)American sign language (ASL) postures The ASL postureswere presented on sheets of paper Here subjects started froman initial posture and stopped at one ASL posture

22 Preprocessing First we calculated angular velocitiesfrom the joint angle profiles collected in the experiment Wepreserved only the relevant projectile movementmdashabout 045second or 39 samples under a sampling rate of 86Hz

Second we constructed an angular velocity matrix 119881

for each subject Angular velocity profiles of the 10 jointscorresponding to one object were cascaded and each rowof the angular velocity matrix represented one movement in

Computational Intelligence and Neuroscience 3

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

PC1minus1 minus05 0 05 1

X1

X2

PC2

(a)

4

38

36

34

32

3

28

26

24

22

2

45 5 55 6 65 7 75 8

X1

X2

(b)

Figure 1 Comparison between PCA and ULDA on one sample data set (a) Two-variable data was analyzed using PCA The figure shows abiplot of principal componentsThemaximum variance is across the horizontal axis or PC1The second highest variance is across the verticalaxis or PC2 (b) The figure shows the linear discriminant that separates the two groups of data The axes represent the two variables 119883

1and

1198832

time The matrix had 100 rows (corresponding to 100 rapidgrasping tasks from first phase) and 39 times 10 = 390 columns

119881

=

[[[[[[[

[

V11(1) sdot sdot sdot V1

1(39) sdot sdot sdot V1

10(1) sdot sdot sdot V1

10(39)

V1198921(1) sdot sdot sdot V119892

1(39) sdot sdot sdot V119892

10(1) sdot sdot sdot V119892

10(39)

V1001

(1) sdot sdot sdot V1001

(39) sdot sdot sdot V10010

(1) sdot sdot sdot V10010

(39)

]]]]]]]

]

(1)

where V119892119894(119905) represents the angular velocity of joint 119894 (119894 =

1 10) at time 119905 (119905 = 1 39) in the 119892th grasping task(119892 = 1 100)

23 Dimensionality Reduction We then performed PCA andULDA on the angular velocity matrix 119881 composed of rapidgrasping tasks to derive kinematic synergies

(1) Principal Component Analysis We implemented PCAusing singular value decomposition (SVD) The angularvelocity matrix 119881 was factorized to three matrices 119880 Σ and119878 as shown

119881 = 119880Σ119878 (2)

where 119880 is a 100-by-100 matrix which has orthonormalcolumns so that 1198801015840119880 = 119868

100times100(100-by-100 identity matrix)

119878 is a 100-by-390 matrix which has orthonormal rows sothat 119878119878

1015840= 119868100times100

and Σ is a 100-by-100 diagonal matrixdiag120582

1 1205822 120582

100 with 120582

1ge 1205822ge sdot sdot sdot ge 120582

100ge 0 Matrix

119881 can be approximated by another matrix with reducedrank 119898 by replacing Σ with Σ

119898 which contains only the 119898

largest singular values that is 1205821 120582

119898(the other singular

values are replaced by zeros) The approximation matrix

can be written in a more compact form

= 119880119898diag 120582

1 120582

119898 119878119898 (3)

where 119880119898

is a 100-by-119898 matrix containing the first 119898

columns of 119880 and 119878119898is a 119898-by-390 matrix containing the

first 119898 rows of 119878 Then each row of 119878119898is called a principal

component (PC) and the product 119880119898diag120582

1 120582

119898 is

called the weight matrixFor easy comparison the elements of 119878

119898in a way similar

to (1) was written as

119878119898

equiv[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(39) sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(39)

119904119898

1(1) sdot sdot sdot 119904

119898

1(39) sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(39)

]]

]

(4)

The angular velocity profiles (obtained by rearranging alljoints row-wise for the PCs)

[[[[[[[

[

119904119895

1(1) sdot sdot sdot 119904

119895

1(39)

119904119895

2(1) sdot sdot sdot 119904

119895

2(39)

119904119895

10(1) sdot sdot sdot 119904

119895

10(39)

]]]]]]]

]

119895 = 1 119898 (5)

can be viewed as synergies Six synergies accounted for 95of variance in the postures

(2) Unsupervised Linear Discriminant AnalysisUnsupervisedlinear discriminant analysis (ULDA) was implemented usinga two-stage process First k-means clusteringmethod createdlabels for the data k-means clustering groups the data bycalculating squared Euclidian distance between the data

4 Computational Intelligence and Neuroscience

points Each centroid is the mean of the points in that groupor cluster Classical LDAwas then used based on these labelsULDA was performed on the angular velocity matrix 119881 For119884 = 119882

119879119881 where 119884 is the transformed matrix and 119882 is

the transformation matrix the optimal transformation usingLDA is obtained by maximizing 119882

lowast as follows

119882lowast

=119882119879119878119861119882

119882119879119878119882119882

(6)

where 119878119861denotes between class covariance and 119878

119882denotes

within class covariance The linear discriminants derivedfrom ULDA were used as new axes The number of lineardiscriminants used was same as the number of principalcomponents being used in comparison

24 Reconstruction of Natural Grasping and ASL PosturalMovements The synergies extracted from PCA and ULDAwere used in reconstruction of natural and ASL movements1198971-norm minimization was used to optimally and sparsely

select the synergies This was similar to the methods in[6] Briefly these were the steps involved in the 119897

1-norm

minimization algorithm Let us assume that for a subject 119898synergies were obtained The duration of the synergies is 119905

119904

samples (119905119904= 39 in this study) Consider an angular velocity

profile of the subject k(119905) 119905 = 1 119879 where 119879 (119879 = 82 inthis study) represents the movement duration (in samples)

This profile can be rewritten as a row vector denoted by krowas follows

krow = [V1(1) V

1(119879) V

10(1) V

10(119879)] (7)

Similarly a synergy s119895(sdot) can be rewritten as the following rowvector

[119904119895

1(1) 119904

119895

1(119905119904) 0 0 119904

119895

10(1) 119904

119895

10(119905119904) 0 0]

(8)

We add 119879 minus 119905119904zeros after each 119904

119895

119894(119905119904) (119894 = 1 10) in the

above vector in order to make the length of the vector thesame as that of krow If the synergy is shifted in time by 119905

119895119896

(0 le 119905119895119896

le 119879 minus 119905119904) samples and then we obtain the following

row vector

[0 0 119904119895

1(1) 119904

119895

1(119905119904) 0 0

0 0 119904119895

10(1) 119904

119895

10(119905119904) 0 0]

(9)

with 119905119895119896zeros added before each 119904

119895

119894(1) and 119879 minus 119905

119904minus 119905119895119896zeros

added after each 119904119895

119894(119905119904)

Then we construct a matrix 119861 consisting of the rowvectors of the synergies and all their possible shifts Thematrix 119861 can be viewed as a bank or library of templates witheach row corresponding to shifted version of synergyThefirstrow contains joint angular velocity profiles of each joint ofthe first synergy Each subsequent row contains time-shiftedversions Consider

119861 equiv

[[[[[[[[[[[[[[[[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904) 0 sdot sdot sdot 0

0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904)

119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904) 0 sdot sdot sdot 0

0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904)

]]]]]]]]]]]]]]]]]

]

(10)

With the above notation we are trying to achieve a linearcombination of synergies that can reconstruct the velocityprofiles as in the following equation

krow = c119861 (11)

where c denotes

[11988810 11988811 119888

1119870 11988820 119888

2119870 119888

119898119870] (12)

where 119888119895119896

represents the weight for 119895th synergy with a shiftof 119905119895119896 The matrix 119861 can be viewed as a bank or library

of template functions with each row of 119861 as a template

krow represents a natural grasp or an ASL postural movementthat is being reconstructed Thus each time-shifted synergyrepresented in 119861 can be used to reconstruct the entiremovement

The following was the optimization problem that wasused in selection of synergies in reconstruction of a particularmovement

Minimize c1 +1

120582

1003817100381710038171003817c119861 minus krow1003817100381710038171003817

2

2 (13)

where sdot 1represents the 119897

1norm sdot

2represents the 119897

2

norm or Euclidean norm of a vector and 120582 is a regulation

Computational Intelligence and Neuroscience 5

parameter Thus the optimization problem solves for cyielding a sparse selection of synergies that minimizes thedifference between the recorded joint angular velocities of anatural grasping movement or ASL postural movement andjoint angular velocities of the reconstructed movement

To evaluate the reconstruction of natural and ASL postu-ral movements the reconstruction error was determined foreach task by

sum119899

119894=1sum119879

119905=1[V119892119894(119905) minus V119892

119894(119905)]2

sum119899

119894=1sum119879

119905=1V119892119894(119905)2

(14)

where V119892119894(119905) (119905 = 1 119879) is the angular velocity profile of

task 119892 and finger joint 119894 (119894 = 1 119899) reconstructed usinga given number of synergies This yields a ratio between theapproximate error and the original angular velocity profileThus an error of 1 represents a squared error of 1 at every timepoint and every task for each joint Presented results shownormalized error where an error of zero is minimum errorcorresponding to best reconstruction and an error of 1 is themaximum error corresponding to worst reconstruction

3 Results

PCA and ULDA described in Section 23 were used to derivekinematic synergies from preprocessed hand joint angularvelocities during rapid grasps The top six significant syner-gies derived from PCA and ULDA were used in reconstruc-tion of natural movements and ASL postural movementsFigure 2 shows a representative example of six synergiesderived from PCA and ULDA for one subject Synergies 1

and 2 derived from PCA show broad bell-shaped velocitypatterns while synergies 1ndash5 derived from ULDA especiallyin PIP joints show distinctly different patterns Interestinglysynergies derived from ULDA show an initial movementdelay which is consistent in PIP joints for synergies 1ndash5 Inboth methods velocity patterns for higher-order synergiesare characterized by multiple submovements Extension isfirst seen in synergy 2 derived from PCA and synergy 6derived from ULDA In terms of joint angular velocitypatterns kinematic synergies further reveal relationshipsfound between joints PIP joints reach a greater velocity thanMCP joints in synergies 1 and 3 Conversely MCP jointsreach a greater velocity than PIP joints in synergies 2 and4 The same inverse relationship where PIP joint reach agreater velocity thanMCP joints is found in synergy 1 derivedfrom ULDA However only synergy 5 shows a movementwhere MCP joints have greater velocities than PIP jointsThese results encourage further analysis on the importanceof each synergy In order to determine how the numberof synergies used in reconstruction affects performance ofeach method we calculated reconstruction errors for up to10 synergies (Figures 3 and 4) In both of these figures wecan see the performance of ULDA plateaus after 4 synergiesReconstruction error continues to decrease for PCA asmore synergies are used It is evident that PCA performsbetter than ULDA in natural grasp reconstruction Howeverreconstruction errors of ASL postural movements are similarfor both methods until 5 synergies are used after which

the performance of ULDA plateaus and PCA error decreases(Figure 4)

Using the optimization algorithm all natural grasps andASL postural movements were reconstructed Figure 5 showsthe mean reconstruction errors for 100 natural movementsacross 10 subjects Error bars indicate the standard deviationacross 10 subjects Similarly Figure 6 shows the mean recon-struction errors for 36 ASL postural movements Error barsindicate the standard deviations across 10 subjects PCA hadthe best overall performancewithmean reconstruction errorsof 008 and 02002 for natural grasping and ASL posturalmovements respectively ULDA has reconstruction error of01867 and 03147 for natural grasping and ASL posturalmovements respectively Green and red arrows indicatemovements that had the best and worst reconstructions forboth methods respectively These reconstructions are shownin Figures 7 and 8 Figure 7 (top) shows a reconstruction ofgrasping task number 47 which had the lowest reconstruc-tion errors for both methods we observe that both methodswere able to reconstruct a natural grasp with minimal errorhowever ULDA was unable to replicate joint extension inthe thumb and pinky PIP joints Figure 7 (bottom) shows areconstruction of a natural grasping task number 75 whichhad the highest reconstruction error for both methods Inthis task the recorded movement (red) lacks smooth velocitypatterns and is also characterized by lower velocities Thistype of movement was also seen in natural grasping tasksnumbered 1 12 17 18 38 49 and 80 Both methods wereunable to replicate this type of movement although PCAhad lower errors Reconstruction errors of ASL posturalmovements were greater than those of natural grasps forboth methods Figure 7 (top) shows the best reconstructionof an ASL postural movement (task number 29) PCA wasunable to replicate themagnitude of velocitywhileULDAwasunable replicate the temporal structure of each joint angularvelocity profile ASL postural movement task number 9 hadthe highest reconstruction error and is shown in Figure 8(bottom) Both methods were unable to replicate extensionthat was not consistent across joint types

4 Discussion

Anatomical neural and functional coupling in the humanhand suggests that all possible hand postures from everydayactivities lie in a lower-dimensional subspace that can becharacterized by kinematic synergies [5] The synergies inthis paper were derived from grasping kinematic data andwere tested for generalizability on ASL postures Principalcomponent analysis was performed on the posture matrix orin otherwords on the high-dimensional space of 100 posturesmeaning the variables here are postures and the observationsare joint angular velocities for these postures The synergiesare principal components that are expressed as weightedlinear combinations of these 100 postures The weightsare derived from eigen vectors As principal componentsrepresent the axes aligned with the directions of maximumvariance the synergies are the most commonly found jointangular velocity patterns used during the 100 postural tasksSix synergies were found to account for 95 of the variance

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

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Human-ComputerInteraction

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2 Computational Intelligence and Neuroscience

successful in natural datasets linear dimensionality reduc-tion methods include nonnegative matrix factorization(NMF) principal component analysis (PCA) and lineardiscriminant analysis (LDA) Ajiboye and Weir [13] usedNMF on mimed American sign language (ASL) postures todetermine muscle synergies and found that subject-specificsynergies were characterized by coactivation of muscleswhile population (similar across all subjects) synergies weretypically dominated by a single muscle PCA has been widelyused to extract postural kinematic and muscle synergies[6 14ndash17] Mason et al [14] used PCA implemented withsingular value decomposition on a set of grasping tasksand found that the first eigenposture resembled a wholehand grasp This is similar to the results by [5 14 15]Tresch et al [18] compared multiple matrix factorizationalgorithms including PCA independent component analysis(ICA) NMF factor analysis (FA) and combinations of theabove to determine muscles synergies He found that thebest performing methods (FA ICA NMF ICAPCA andprobabilistic ICA) identified similar synergies Dimensional-ity reduction methods not only yield significant eigenvectorsfromphysiological data but also reflect patterns inmovementgeneration Hence two contrasting dimensionality reductionmethods such as PCA and LDA may be partial towards dif-ferent kinematic movement primitives By comparing thesetwo methods we can determine which kinematic propertiesare most important in movement generation

PCA attempts to accurately represent the data in low-dimensional space by projecting the data in the directions ofmaximum variance as shown in Figure 1(a) PCA performedon a sample dataset is shown hereThe first principal compo-nent axis corresponds to the direction of maximum varianceof the data and similarly second and third in the decreasingorder LDA was used to classify the same sample dataset(Figure 1(b)) Directions of maximum variance as seen inPCA are not useful for classification Hence LDA projectsthe data in directions that preserve maximum separationor discrimination in groups or classes of data LDA seeksdimensionality reduction while preserving as much classdiscrimination as possible

In this paper we compared two contrasting methodsPCA and LDA in deriving synergies and evaluated themon a set of natural grasping and ASL postural movementsBoth PCA and LDA are linear dimensionality reductionmethods that reduce high-dimensional movements of thehand by looking for either most common patterns (PCA) ordistinct separable patterns (LDA) While previous researchhas identified a limited number of discriminatingmuscles in asingle synergy such patterns have not been seen in kinematicspace As LDA aims to separate data resulting synergies mayreflect distinct patterns Although LDA is a type of clusteringmethod it offers a direct contrast to PCA separating variance(LDA) ormaximizing variance (PCA)Thus we can interpretthe strengths and weaknesses of both methods In orderto maintain fairness in comparison with PCA which is anunsupervised method LDA used in this paper was alsounsupervised (ULDA) first by labeling the data with k-meansclustering and then classifying it using classical LDA

2 Methods

21 Materials and Experiment In the experiment we used aCyberGlove (CyberGlove Systems LLC San Jose CA USA)equipped with 22 sensors that captured hand movementsat a sampling frequency of 86Hz In this paper we onlyconsidered 10 of the sensors which measure the angles of thecarpometacarpal (CMC)metacarpophalangeal (MCP) jointsof the thumb and the MCP and proximal interphalangeal(PIP) joints of the other four fingers These 10 joints cancapture most characteristics of the hand in grasping tasksWe used several objects of different shapes (spheres circulardiscs rectangles pentagons nuts and bolts) and differentdimensions (spheres 1ndash5 cm in radius discs 2ndash10 cm inradius rectangles and pentagons 1ndash3 cm each side nuts andbolts 2ndash5 cm in length) in the grasping tasks 10 subjectsparticipated in this experiment after signing the consentforms approved by the Institutional Review Board (IRB) ofthe University of Pittsburgh

A typical task consisted of grasping the above objectsStart and stop times of each task were signaled by computer-generated beeps In each task the subject was in a seatedposition resting hisher right hand at a corner of a table andupon hearing the beep and grasped the object placed onthe table At the time of the start beep the hand was in restposture and then the subject grasped the object and held ituntil the stop beep

In the first phase subjects were instructed to rapidly grasp50 objects one at a time This was repeated for the same 50objects and thus the whole training phase obtained 100 rapidgrasps Rapid grasping movements from the first phase wereused in deriving synergies We assume that by minimizingreaction time and minimizing continuous sensory feedbackthe resulting task space is driven by synchronous weightedsynergies resulting from impulses originating in a higherlevel of neural system The rapid movement is achieved asa weighted sum of synchronous synergies Only these 100rapid grasps were used in extracting synergies using PCA andULDA

In the second phase subjects were instructed to graspthe above 50 objects naturally (slower than the rapid grasps)and then this was repeated So far the tasks involved onlygrasping In the third phase to test the generalizability ofthe synergies over a broad range of postures subjects werealso asked to imitate 36 (10 numbers and 26 alphabet letters)American sign language (ASL) postures The ASL postureswere presented on sheets of paper Here subjects started froman initial posture and stopped at one ASL posture

22 Preprocessing First we calculated angular velocitiesfrom the joint angle profiles collected in the experiment Wepreserved only the relevant projectile movementmdashabout 045second or 39 samples under a sampling rate of 86Hz

Second we constructed an angular velocity matrix 119881

for each subject Angular velocity profiles of the 10 jointscorresponding to one object were cascaded and each rowof the angular velocity matrix represented one movement in

Computational Intelligence and Neuroscience 3

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

PC1minus1 minus05 0 05 1

X1

X2

PC2

(a)

4

38

36

34

32

3

28

26

24

22

2

45 5 55 6 65 7 75 8

X1

X2

(b)

Figure 1 Comparison between PCA and ULDA on one sample data set (a) Two-variable data was analyzed using PCA The figure shows abiplot of principal componentsThemaximum variance is across the horizontal axis or PC1The second highest variance is across the verticalaxis or PC2 (b) The figure shows the linear discriminant that separates the two groups of data The axes represent the two variables 119883

1and

1198832

time The matrix had 100 rows (corresponding to 100 rapidgrasping tasks from first phase) and 39 times 10 = 390 columns

119881

=

[[[[[[[

[

V11(1) sdot sdot sdot V1

1(39) sdot sdot sdot V1

10(1) sdot sdot sdot V1

10(39)

V1198921(1) sdot sdot sdot V119892

1(39) sdot sdot sdot V119892

10(1) sdot sdot sdot V119892

10(39)

V1001

(1) sdot sdot sdot V1001

(39) sdot sdot sdot V10010

(1) sdot sdot sdot V10010

(39)

]]]]]]]

]

(1)

where V119892119894(119905) represents the angular velocity of joint 119894 (119894 =

1 10) at time 119905 (119905 = 1 39) in the 119892th grasping task(119892 = 1 100)

23 Dimensionality Reduction We then performed PCA andULDA on the angular velocity matrix 119881 composed of rapidgrasping tasks to derive kinematic synergies

(1) Principal Component Analysis We implemented PCAusing singular value decomposition (SVD) The angularvelocity matrix 119881 was factorized to three matrices 119880 Σ and119878 as shown

119881 = 119880Σ119878 (2)

where 119880 is a 100-by-100 matrix which has orthonormalcolumns so that 1198801015840119880 = 119868

100times100(100-by-100 identity matrix)

119878 is a 100-by-390 matrix which has orthonormal rows sothat 119878119878

1015840= 119868100times100

and Σ is a 100-by-100 diagonal matrixdiag120582

1 1205822 120582

100 with 120582

1ge 1205822ge sdot sdot sdot ge 120582

100ge 0 Matrix

119881 can be approximated by another matrix with reducedrank 119898 by replacing Σ with Σ

119898 which contains only the 119898

largest singular values that is 1205821 120582

119898(the other singular

values are replaced by zeros) The approximation matrix

can be written in a more compact form

= 119880119898diag 120582

1 120582

119898 119878119898 (3)

where 119880119898

is a 100-by-119898 matrix containing the first 119898

columns of 119880 and 119878119898is a 119898-by-390 matrix containing the

first 119898 rows of 119878 Then each row of 119878119898is called a principal

component (PC) and the product 119880119898diag120582

1 120582

119898 is

called the weight matrixFor easy comparison the elements of 119878

119898in a way similar

to (1) was written as

119878119898

equiv[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(39) sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(39)

119904119898

1(1) sdot sdot sdot 119904

119898

1(39) sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(39)

]]

]

(4)

The angular velocity profiles (obtained by rearranging alljoints row-wise for the PCs)

[[[[[[[

[

119904119895

1(1) sdot sdot sdot 119904

119895

1(39)

119904119895

2(1) sdot sdot sdot 119904

119895

2(39)

119904119895

10(1) sdot sdot sdot 119904

119895

10(39)

]]]]]]]

]

119895 = 1 119898 (5)

can be viewed as synergies Six synergies accounted for 95of variance in the postures

(2) Unsupervised Linear Discriminant AnalysisUnsupervisedlinear discriminant analysis (ULDA) was implemented usinga two-stage process First k-means clusteringmethod createdlabels for the data k-means clustering groups the data bycalculating squared Euclidian distance between the data

4 Computational Intelligence and Neuroscience

points Each centroid is the mean of the points in that groupor cluster Classical LDAwas then used based on these labelsULDA was performed on the angular velocity matrix 119881 For119884 = 119882

119879119881 where 119884 is the transformed matrix and 119882 is

the transformation matrix the optimal transformation usingLDA is obtained by maximizing 119882

lowast as follows

119882lowast

=119882119879119878119861119882

119882119879119878119882119882

(6)

where 119878119861denotes between class covariance and 119878

119882denotes

within class covariance The linear discriminants derivedfrom ULDA were used as new axes The number of lineardiscriminants used was same as the number of principalcomponents being used in comparison

24 Reconstruction of Natural Grasping and ASL PosturalMovements The synergies extracted from PCA and ULDAwere used in reconstruction of natural and ASL movements1198971-norm minimization was used to optimally and sparsely

select the synergies This was similar to the methods in[6] Briefly these were the steps involved in the 119897

1-norm

minimization algorithm Let us assume that for a subject 119898synergies were obtained The duration of the synergies is 119905

119904

samples (119905119904= 39 in this study) Consider an angular velocity

profile of the subject k(119905) 119905 = 1 119879 where 119879 (119879 = 82 inthis study) represents the movement duration (in samples)

This profile can be rewritten as a row vector denoted by krowas follows

krow = [V1(1) V

1(119879) V

10(1) V

10(119879)] (7)

Similarly a synergy s119895(sdot) can be rewritten as the following rowvector

[119904119895

1(1) 119904

119895

1(119905119904) 0 0 119904

119895

10(1) 119904

119895

10(119905119904) 0 0]

(8)

We add 119879 minus 119905119904zeros after each 119904

119895

119894(119905119904) (119894 = 1 10) in the

above vector in order to make the length of the vector thesame as that of krow If the synergy is shifted in time by 119905

119895119896

(0 le 119905119895119896

le 119879 minus 119905119904) samples and then we obtain the following

row vector

[0 0 119904119895

1(1) 119904

119895

1(119905119904) 0 0

0 0 119904119895

10(1) 119904

119895

10(119905119904) 0 0]

(9)

with 119905119895119896zeros added before each 119904

119895

119894(1) and 119879 minus 119905

119904minus 119905119895119896zeros

added after each 119904119895

119894(119905119904)

Then we construct a matrix 119861 consisting of the rowvectors of the synergies and all their possible shifts Thematrix 119861 can be viewed as a bank or library of templates witheach row corresponding to shifted version of synergyThefirstrow contains joint angular velocity profiles of each joint ofthe first synergy Each subsequent row contains time-shiftedversions Consider

119861 equiv

[[[[[[[[[[[[[[[[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904) 0 sdot sdot sdot 0

0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904)

119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904) 0 sdot sdot sdot 0

0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904)

]]]]]]]]]]]]]]]]]

]

(10)

With the above notation we are trying to achieve a linearcombination of synergies that can reconstruct the velocityprofiles as in the following equation

krow = c119861 (11)

where c denotes

[11988810 11988811 119888

1119870 11988820 119888

2119870 119888

119898119870] (12)

where 119888119895119896

represents the weight for 119895th synergy with a shiftof 119905119895119896 The matrix 119861 can be viewed as a bank or library

of template functions with each row of 119861 as a template

krow represents a natural grasp or an ASL postural movementthat is being reconstructed Thus each time-shifted synergyrepresented in 119861 can be used to reconstruct the entiremovement

The following was the optimization problem that wasused in selection of synergies in reconstruction of a particularmovement

Minimize c1 +1

120582

1003817100381710038171003817c119861 minus krow1003817100381710038171003817

2

2 (13)

where sdot 1represents the 119897

1norm sdot

2represents the 119897

2

norm or Euclidean norm of a vector and 120582 is a regulation

Computational Intelligence and Neuroscience 5

parameter Thus the optimization problem solves for cyielding a sparse selection of synergies that minimizes thedifference between the recorded joint angular velocities of anatural grasping movement or ASL postural movement andjoint angular velocities of the reconstructed movement

To evaluate the reconstruction of natural and ASL postu-ral movements the reconstruction error was determined foreach task by

sum119899

119894=1sum119879

119905=1[V119892119894(119905) minus V119892

119894(119905)]2

sum119899

119894=1sum119879

119905=1V119892119894(119905)2

(14)

where V119892119894(119905) (119905 = 1 119879) is the angular velocity profile of

task 119892 and finger joint 119894 (119894 = 1 119899) reconstructed usinga given number of synergies This yields a ratio between theapproximate error and the original angular velocity profileThus an error of 1 represents a squared error of 1 at every timepoint and every task for each joint Presented results shownormalized error where an error of zero is minimum errorcorresponding to best reconstruction and an error of 1 is themaximum error corresponding to worst reconstruction

3 Results

PCA and ULDA described in Section 23 were used to derivekinematic synergies from preprocessed hand joint angularvelocities during rapid grasps The top six significant syner-gies derived from PCA and ULDA were used in reconstruc-tion of natural movements and ASL postural movementsFigure 2 shows a representative example of six synergiesderived from PCA and ULDA for one subject Synergies 1

and 2 derived from PCA show broad bell-shaped velocitypatterns while synergies 1ndash5 derived from ULDA especiallyin PIP joints show distinctly different patterns Interestinglysynergies derived from ULDA show an initial movementdelay which is consistent in PIP joints for synergies 1ndash5 Inboth methods velocity patterns for higher-order synergiesare characterized by multiple submovements Extension isfirst seen in synergy 2 derived from PCA and synergy 6derived from ULDA In terms of joint angular velocitypatterns kinematic synergies further reveal relationshipsfound between joints PIP joints reach a greater velocity thanMCP joints in synergies 1 and 3 Conversely MCP jointsreach a greater velocity than PIP joints in synergies 2 and4 The same inverse relationship where PIP joint reach agreater velocity thanMCP joints is found in synergy 1 derivedfrom ULDA However only synergy 5 shows a movementwhere MCP joints have greater velocities than PIP jointsThese results encourage further analysis on the importanceof each synergy In order to determine how the numberof synergies used in reconstruction affects performance ofeach method we calculated reconstruction errors for up to10 synergies (Figures 3 and 4) In both of these figures wecan see the performance of ULDA plateaus after 4 synergiesReconstruction error continues to decrease for PCA asmore synergies are used It is evident that PCA performsbetter than ULDA in natural grasp reconstruction Howeverreconstruction errors of ASL postural movements are similarfor both methods until 5 synergies are used after which

the performance of ULDA plateaus and PCA error decreases(Figure 4)

Using the optimization algorithm all natural grasps andASL postural movements were reconstructed Figure 5 showsthe mean reconstruction errors for 100 natural movementsacross 10 subjects Error bars indicate the standard deviationacross 10 subjects Similarly Figure 6 shows the mean recon-struction errors for 36 ASL postural movements Error barsindicate the standard deviations across 10 subjects PCA hadthe best overall performancewithmean reconstruction errorsof 008 and 02002 for natural grasping and ASL posturalmovements respectively ULDA has reconstruction error of01867 and 03147 for natural grasping and ASL posturalmovements respectively Green and red arrows indicatemovements that had the best and worst reconstructions forboth methods respectively These reconstructions are shownin Figures 7 and 8 Figure 7 (top) shows a reconstruction ofgrasping task number 47 which had the lowest reconstruc-tion errors for both methods we observe that both methodswere able to reconstruct a natural grasp with minimal errorhowever ULDA was unable to replicate joint extension inthe thumb and pinky PIP joints Figure 7 (bottom) shows areconstruction of a natural grasping task number 75 whichhad the highest reconstruction error for both methods Inthis task the recorded movement (red) lacks smooth velocitypatterns and is also characterized by lower velocities Thistype of movement was also seen in natural grasping tasksnumbered 1 12 17 18 38 49 and 80 Both methods wereunable to replicate this type of movement although PCAhad lower errors Reconstruction errors of ASL posturalmovements were greater than those of natural grasps forboth methods Figure 7 (top) shows the best reconstructionof an ASL postural movement (task number 29) PCA wasunable to replicate themagnitude of velocitywhileULDAwasunable replicate the temporal structure of each joint angularvelocity profile ASL postural movement task number 9 hadthe highest reconstruction error and is shown in Figure 8(bottom) Both methods were unable to replicate extensionthat was not consistent across joint types

4 Discussion

Anatomical neural and functional coupling in the humanhand suggests that all possible hand postures from everydayactivities lie in a lower-dimensional subspace that can becharacterized by kinematic synergies [5] The synergies inthis paper were derived from grasping kinematic data andwere tested for generalizability on ASL postures Principalcomponent analysis was performed on the posture matrix orin otherwords on the high-dimensional space of 100 posturesmeaning the variables here are postures and the observationsare joint angular velocities for these postures The synergiesare principal components that are expressed as weightedlinear combinations of these 100 postures The weightsare derived from eigen vectors As principal componentsrepresent the axes aligned with the directions of maximumvariance the synergies are the most commonly found jointangular velocity patterns used during the 100 postural tasksSix synergies were found to account for 95 of the variance

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

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Human-ComputerInteraction

Advances in

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Computational Intelligence and Neuroscience 3

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

PC1minus1 minus05 0 05 1

X1

X2

PC2

(a)

4

38

36

34

32

3

28

26

24

22

2

45 5 55 6 65 7 75 8

X1

X2

(b)

Figure 1 Comparison between PCA and ULDA on one sample data set (a) Two-variable data was analyzed using PCA The figure shows abiplot of principal componentsThemaximum variance is across the horizontal axis or PC1The second highest variance is across the verticalaxis or PC2 (b) The figure shows the linear discriminant that separates the two groups of data The axes represent the two variables 119883

1and

1198832

time The matrix had 100 rows (corresponding to 100 rapidgrasping tasks from first phase) and 39 times 10 = 390 columns

119881

=

[[[[[[[

[

V11(1) sdot sdot sdot V1

1(39) sdot sdot sdot V1

10(1) sdot sdot sdot V1

10(39)

V1198921(1) sdot sdot sdot V119892

1(39) sdot sdot sdot V119892

10(1) sdot sdot sdot V119892

10(39)

V1001

(1) sdot sdot sdot V1001

(39) sdot sdot sdot V10010

(1) sdot sdot sdot V10010

(39)

]]]]]]]

]

(1)

where V119892119894(119905) represents the angular velocity of joint 119894 (119894 =

1 10) at time 119905 (119905 = 1 39) in the 119892th grasping task(119892 = 1 100)

23 Dimensionality Reduction We then performed PCA andULDA on the angular velocity matrix 119881 composed of rapidgrasping tasks to derive kinematic synergies

(1) Principal Component Analysis We implemented PCAusing singular value decomposition (SVD) The angularvelocity matrix 119881 was factorized to three matrices 119880 Σ and119878 as shown

119881 = 119880Σ119878 (2)

where 119880 is a 100-by-100 matrix which has orthonormalcolumns so that 1198801015840119880 = 119868

100times100(100-by-100 identity matrix)

119878 is a 100-by-390 matrix which has orthonormal rows sothat 119878119878

1015840= 119868100times100

and Σ is a 100-by-100 diagonal matrixdiag120582

1 1205822 120582

100 with 120582

1ge 1205822ge sdot sdot sdot ge 120582

100ge 0 Matrix

119881 can be approximated by another matrix with reducedrank 119898 by replacing Σ with Σ

119898 which contains only the 119898

largest singular values that is 1205821 120582

119898(the other singular

values are replaced by zeros) The approximation matrix

can be written in a more compact form

= 119880119898diag 120582

1 120582

119898 119878119898 (3)

where 119880119898

is a 100-by-119898 matrix containing the first 119898

columns of 119880 and 119878119898is a 119898-by-390 matrix containing the

first 119898 rows of 119878 Then each row of 119878119898is called a principal

component (PC) and the product 119880119898diag120582

1 120582

119898 is

called the weight matrixFor easy comparison the elements of 119878

119898in a way similar

to (1) was written as

119878119898

equiv[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(39) sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(39)

119904119898

1(1) sdot sdot sdot 119904

119898

1(39) sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(39)

]]

]

(4)

The angular velocity profiles (obtained by rearranging alljoints row-wise for the PCs)

[[[[[[[

[

119904119895

1(1) sdot sdot sdot 119904

119895

1(39)

119904119895

2(1) sdot sdot sdot 119904

119895

2(39)

119904119895

10(1) sdot sdot sdot 119904

119895

10(39)

]]]]]]]

]

119895 = 1 119898 (5)

can be viewed as synergies Six synergies accounted for 95of variance in the postures

(2) Unsupervised Linear Discriminant AnalysisUnsupervisedlinear discriminant analysis (ULDA) was implemented usinga two-stage process First k-means clusteringmethod createdlabels for the data k-means clustering groups the data bycalculating squared Euclidian distance between the data

4 Computational Intelligence and Neuroscience

points Each centroid is the mean of the points in that groupor cluster Classical LDAwas then used based on these labelsULDA was performed on the angular velocity matrix 119881 For119884 = 119882

119879119881 where 119884 is the transformed matrix and 119882 is

the transformation matrix the optimal transformation usingLDA is obtained by maximizing 119882

lowast as follows

119882lowast

=119882119879119878119861119882

119882119879119878119882119882

(6)

where 119878119861denotes between class covariance and 119878

119882denotes

within class covariance The linear discriminants derivedfrom ULDA were used as new axes The number of lineardiscriminants used was same as the number of principalcomponents being used in comparison

24 Reconstruction of Natural Grasping and ASL PosturalMovements The synergies extracted from PCA and ULDAwere used in reconstruction of natural and ASL movements1198971-norm minimization was used to optimally and sparsely

select the synergies This was similar to the methods in[6] Briefly these were the steps involved in the 119897

1-norm

minimization algorithm Let us assume that for a subject 119898synergies were obtained The duration of the synergies is 119905

119904

samples (119905119904= 39 in this study) Consider an angular velocity

profile of the subject k(119905) 119905 = 1 119879 where 119879 (119879 = 82 inthis study) represents the movement duration (in samples)

This profile can be rewritten as a row vector denoted by krowas follows

krow = [V1(1) V

1(119879) V

10(1) V

10(119879)] (7)

Similarly a synergy s119895(sdot) can be rewritten as the following rowvector

[119904119895

1(1) 119904

119895

1(119905119904) 0 0 119904

119895

10(1) 119904

119895

10(119905119904) 0 0]

(8)

We add 119879 minus 119905119904zeros after each 119904

119895

119894(119905119904) (119894 = 1 10) in the

above vector in order to make the length of the vector thesame as that of krow If the synergy is shifted in time by 119905

119895119896

(0 le 119905119895119896

le 119879 minus 119905119904) samples and then we obtain the following

row vector

[0 0 119904119895

1(1) 119904

119895

1(119905119904) 0 0

0 0 119904119895

10(1) 119904

119895

10(119905119904) 0 0]

(9)

with 119905119895119896zeros added before each 119904

119895

119894(1) and 119879 minus 119905

119904minus 119905119895119896zeros

added after each 119904119895

119894(119905119904)

Then we construct a matrix 119861 consisting of the rowvectors of the synergies and all their possible shifts Thematrix 119861 can be viewed as a bank or library of templates witheach row corresponding to shifted version of synergyThefirstrow contains joint angular velocity profiles of each joint ofthe first synergy Each subsequent row contains time-shiftedversions Consider

119861 equiv

[[[[[[[[[[[[[[[[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904) 0 sdot sdot sdot 0

0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904)

119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904) 0 sdot sdot sdot 0

0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904)

]]]]]]]]]]]]]]]]]

]

(10)

With the above notation we are trying to achieve a linearcombination of synergies that can reconstruct the velocityprofiles as in the following equation

krow = c119861 (11)

where c denotes

[11988810 11988811 119888

1119870 11988820 119888

2119870 119888

119898119870] (12)

where 119888119895119896

represents the weight for 119895th synergy with a shiftof 119905119895119896 The matrix 119861 can be viewed as a bank or library

of template functions with each row of 119861 as a template

krow represents a natural grasp or an ASL postural movementthat is being reconstructed Thus each time-shifted synergyrepresented in 119861 can be used to reconstruct the entiremovement

The following was the optimization problem that wasused in selection of synergies in reconstruction of a particularmovement

Minimize c1 +1

120582

1003817100381710038171003817c119861 minus krow1003817100381710038171003817

2

2 (13)

where sdot 1represents the 119897

1norm sdot

2represents the 119897

2

norm or Euclidean norm of a vector and 120582 is a regulation

Computational Intelligence and Neuroscience 5

parameter Thus the optimization problem solves for cyielding a sparse selection of synergies that minimizes thedifference between the recorded joint angular velocities of anatural grasping movement or ASL postural movement andjoint angular velocities of the reconstructed movement

To evaluate the reconstruction of natural and ASL postu-ral movements the reconstruction error was determined foreach task by

sum119899

119894=1sum119879

119905=1[V119892119894(119905) minus V119892

119894(119905)]2

sum119899

119894=1sum119879

119905=1V119892119894(119905)2

(14)

where V119892119894(119905) (119905 = 1 119879) is the angular velocity profile of

task 119892 and finger joint 119894 (119894 = 1 119899) reconstructed usinga given number of synergies This yields a ratio between theapproximate error and the original angular velocity profileThus an error of 1 represents a squared error of 1 at every timepoint and every task for each joint Presented results shownormalized error where an error of zero is minimum errorcorresponding to best reconstruction and an error of 1 is themaximum error corresponding to worst reconstruction

3 Results

PCA and ULDA described in Section 23 were used to derivekinematic synergies from preprocessed hand joint angularvelocities during rapid grasps The top six significant syner-gies derived from PCA and ULDA were used in reconstruc-tion of natural movements and ASL postural movementsFigure 2 shows a representative example of six synergiesderived from PCA and ULDA for one subject Synergies 1

and 2 derived from PCA show broad bell-shaped velocitypatterns while synergies 1ndash5 derived from ULDA especiallyin PIP joints show distinctly different patterns Interestinglysynergies derived from ULDA show an initial movementdelay which is consistent in PIP joints for synergies 1ndash5 Inboth methods velocity patterns for higher-order synergiesare characterized by multiple submovements Extension isfirst seen in synergy 2 derived from PCA and synergy 6derived from ULDA In terms of joint angular velocitypatterns kinematic synergies further reveal relationshipsfound between joints PIP joints reach a greater velocity thanMCP joints in synergies 1 and 3 Conversely MCP jointsreach a greater velocity than PIP joints in synergies 2 and4 The same inverse relationship where PIP joint reach agreater velocity thanMCP joints is found in synergy 1 derivedfrom ULDA However only synergy 5 shows a movementwhere MCP joints have greater velocities than PIP jointsThese results encourage further analysis on the importanceof each synergy In order to determine how the numberof synergies used in reconstruction affects performance ofeach method we calculated reconstruction errors for up to10 synergies (Figures 3 and 4) In both of these figures wecan see the performance of ULDA plateaus after 4 synergiesReconstruction error continues to decrease for PCA asmore synergies are used It is evident that PCA performsbetter than ULDA in natural grasp reconstruction Howeverreconstruction errors of ASL postural movements are similarfor both methods until 5 synergies are used after which

the performance of ULDA plateaus and PCA error decreases(Figure 4)

Using the optimization algorithm all natural grasps andASL postural movements were reconstructed Figure 5 showsthe mean reconstruction errors for 100 natural movementsacross 10 subjects Error bars indicate the standard deviationacross 10 subjects Similarly Figure 6 shows the mean recon-struction errors for 36 ASL postural movements Error barsindicate the standard deviations across 10 subjects PCA hadthe best overall performancewithmean reconstruction errorsof 008 and 02002 for natural grasping and ASL posturalmovements respectively ULDA has reconstruction error of01867 and 03147 for natural grasping and ASL posturalmovements respectively Green and red arrows indicatemovements that had the best and worst reconstructions forboth methods respectively These reconstructions are shownin Figures 7 and 8 Figure 7 (top) shows a reconstruction ofgrasping task number 47 which had the lowest reconstruc-tion errors for both methods we observe that both methodswere able to reconstruct a natural grasp with minimal errorhowever ULDA was unable to replicate joint extension inthe thumb and pinky PIP joints Figure 7 (bottom) shows areconstruction of a natural grasping task number 75 whichhad the highest reconstruction error for both methods Inthis task the recorded movement (red) lacks smooth velocitypatterns and is also characterized by lower velocities Thistype of movement was also seen in natural grasping tasksnumbered 1 12 17 18 38 49 and 80 Both methods wereunable to replicate this type of movement although PCAhad lower errors Reconstruction errors of ASL posturalmovements were greater than those of natural grasps forboth methods Figure 7 (top) shows the best reconstructionof an ASL postural movement (task number 29) PCA wasunable to replicate themagnitude of velocitywhileULDAwasunable replicate the temporal structure of each joint angularvelocity profile ASL postural movement task number 9 hadthe highest reconstruction error and is shown in Figure 8(bottom) Both methods were unable to replicate extensionthat was not consistent across joint types

4 Discussion

Anatomical neural and functional coupling in the humanhand suggests that all possible hand postures from everydayactivities lie in a lower-dimensional subspace that can becharacterized by kinematic synergies [5] The synergies inthis paper were derived from grasping kinematic data andwere tested for generalizability on ASL postures Principalcomponent analysis was performed on the posture matrix orin otherwords on the high-dimensional space of 100 posturesmeaning the variables here are postures and the observationsare joint angular velocities for these postures The synergiesare principal components that are expressed as weightedlinear combinations of these 100 postures The weightsare derived from eigen vectors As principal componentsrepresent the axes aligned with the directions of maximumvariance the synergies are the most commonly found jointangular velocity patterns used during the 100 postural tasksSix synergies were found to account for 95 of the variance

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

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4 Computational Intelligence and Neuroscience

points Each centroid is the mean of the points in that groupor cluster Classical LDAwas then used based on these labelsULDA was performed on the angular velocity matrix 119881 For119884 = 119882

119879119881 where 119884 is the transformed matrix and 119882 is

the transformation matrix the optimal transformation usingLDA is obtained by maximizing 119882

lowast as follows

119882lowast

=119882119879119878119861119882

119882119879119878119882119882

(6)

where 119878119861denotes between class covariance and 119878

119882denotes

within class covariance The linear discriminants derivedfrom ULDA were used as new axes The number of lineardiscriminants used was same as the number of principalcomponents being used in comparison

24 Reconstruction of Natural Grasping and ASL PosturalMovements The synergies extracted from PCA and ULDAwere used in reconstruction of natural and ASL movements1198971-norm minimization was used to optimally and sparsely

select the synergies This was similar to the methods in[6] Briefly these were the steps involved in the 119897

1-norm

minimization algorithm Let us assume that for a subject 119898synergies were obtained The duration of the synergies is 119905

119904

samples (119905119904= 39 in this study) Consider an angular velocity

profile of the subject k(119905) 119905 = 1 119879 where 119879 (119879 = 82 inthis study) represents the movement duration (in samples)

This profile can be rewritten as a row vector denoted by krowas follows

krow = [V1(1) V

1(119879) V

10(1) V

10(119879)] (7)

Similarly a synergy s119895(sdot) can be rewritten as the following rowvector

[119904119895

1(1) 119904

119895

1(119905119904) 0 0 119904

119895

10(1) 119904

119895

10(119905119904) 0 0]

(8)

We add 119879 minus 119905119904zeros after each 119904

119895

119894(119905119904) (119894 = 1 10) in the

above vector in order to make the length of the vector thesame as that of krow If the synergy is shifted in time by 119905

119895119896

(0 le 119905119895119896

le 119879 minus 119905119904) samples and then we obtain the following

row vector

[0 0 119904119895

1(1) 119904

119895

1(119905119904) 0 0

0 0 119904119895

10(1) 119904

119895

10(119905119904) 0 0]

(9)

with 119905119895119896zeros added before each 119904

119895

119894(1) and 119879 minus 119905

119904minus 119905119895119896zeros

added after each 119904119895

119894(119905119904)

Then we construct a matrix 119861 consisting of the rowvectors of the synergies and all their possible shifts Thematrix 119861 can be viewed as a bank or library of templates witheach row corresponding to shifted version of synergyThefirstrow contains joint angular velocity profiles of each joint ofthe first synergy Each subsequent row contains time-shiftedversions Consider

119861 equiv

[[[[[[[[[[[[[[[[[

[

1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904) 0 sdot sdot sdot 0

0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 1199041

1(1) sdot sdot sdot 119904

1

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

1

10(1) sdot sdot sdot 119904

1

10(119905119904)

119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) 0 sdot sdot sdot 0 sdot sdot sdot 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904) 0 sdot sdot sdot 0

0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0

d d d d sdot sdot sdot

d d d d

0 sdot sdot sdot 0 119904119898

1(1) sdot sdot sdot 119904

119898

1(119905119904) sdot sdot sdot 0 sdot sdot sdot 0 119904

119898

10(1) sdot sdot sdot 119904

119898

10(119905119904)

]]]]]]]]]]]]]]]]]

]

(10)

With the above notation we are trying to achieve a linearcombination of synergies that can reconstruct the velocityprofiles as in the following equation

krow = c119861 (11)

where c denotes

[11988810 11988811 119888

1119870 11988820 119888

2119870 119888

119898119870] (12)

where 119888119895119896

represents the weight for 119895th synergy with a shiftof 119905119895119896 The matrix 119861 can be viewed as a bank or library

of template functions with each row of 119861 as a template

krow represents a natural grasp or an ASL postural movementthat is being reconstructed Thus each time-shifted synergyrepresented in 119861 can be used to reconstruct the entiremovement

The following was the optimization problem that wasused in selection of synergies in reconstruction of a particularmovement

Minimize c1 +1

120582

1003817100381710038171003817c119861 minus krow1003817100381710038171003817

2

2 (13)

where sdot 1represents the 119897

1norm sdot

2represents the 119897

2

norm or Euclidean norm of a vector and 120582 is a regulation

Computational Intelligence and Neuroscience 5

parameter Thus the optimization problem solves for cyielding a sparse selection of synergies that minimizes thedifference between the recorded joint angular velocities of anatural grasping movement or ASL postural movement andjoint angular velocities of the reconstructed movement

To evaluate the reconstruction of natural and ASL postu-ral movements the reconstruction error was determined foreach task by

sum119899

119894=1sum119879

119905=1[V119892119894(119905) minus V119892

119894(119905)]2

sum119899

119894=1sum119879

119905=1V119892119894(119905)2

(14)

where V119892119894(119905) (119905 = 1 119879) is the angular velocity profile of

task 119892 and finger joint 119894 (119894 = 1 119899) reconstructed usinga given number of synergies This yields a ratio between theapproximate error and the original angular velocity profileThus an error of 1 represents a squared error of 1 at every timepoint and every task for each joint Presented results shownormalized error where an error of zero is minimum errorcorresponding to best reconstruction and an error of 1 is themaximum error corresponding to worst reconstruction

3 Results

PCA and ULDA described in Section 23 were used to derivekinematic synergies from preprocessed hand joint angularvelocities during rapid grasps The top six significant syner-gies derived from PCA and ULDA were used in reconstruc-tion of natural movements and ASL postural movementsFigure 2 shows a representative example of six synergiesderived from PCA and ULDA for one subject Synergies 1

and 2 derived from PCA show broad bell-shaped velocitypatterns while synergies 1ndash5 derived from ULDA especiallyin PIP joints show distinctly different patterns Interestinglysynergies derived from ULDA show an initial movementdelay which is consistent in PIP joints for synergies 1ndash5 Inboth methods velocity patterns for higher-order synergiesare characterized by multiple submovements Extension isfirst seen in synergy 2 derived from PCA and synergy 6derived from ULDA In terms of joint angular velocitypatterns kinematic synergies further reveal relationshipsfound between joints PIP joints reach a greater velocity thanMCP joints in synergies 1 and 3 Conversely MCP jointsreach a greater velocity than PIP joints in synergies 2 and4 The same inverse relationship where PIP joint reach agreater velocity thanMCP joints is found in synergy 1 derivedfrom ULDA However only synergy 5 shows a movementwhere MCP joints have greater velocities than PIP jointsThese results encourage further analysis on the importanceof each synergy In order to determine how the numberof synergies used in reconstruction affects performance ofeach method we calculated reconstruction errors for up to10 synergies (Figures 3 and 4) In both of these figures wecan see the performance of ULDA plateaus after 4 synergiesReconstruction error continues to decrease for PCA asmore synergies are used It is evident that PCA performsbetter than ULDA in natural grasp reconstruction Howeverreconstruction errors of ASL postural movements are similarfor both methods until 5 synergies are used after which

the performance of ULDA plateaus and PCA error decreases(Figure 4)

Using the optimization algorithm all natural grasps andASL postural movements were reconstructed Figure 5 showsthe mean reconstruction errors for 100 natural movementsacross 10 subjects Error bars indicate the standard deviationacross 10 subjects Similarly Figure 6 shows the mean recon-struction errors for 36 ASL postural movements Error barsindicate the standard deviations across 10 subjects PCA hadthe best overall performancewithmean reconstruction errorsof 008 and 02002 for natural grasping and ASL posturalmovements respectively ULDA has reconstruction error of01867 and 03147 for natural grasping and ASL posturalmovements respectively Green and red arrows indicatemovements that had the best and worst reconstructions forboth methods respectively These reconstructions are shownin Figures 7 and 8 Figure 7 (top) shows a reconstruction ofgrasping task number 47 which had the lowest reconstruc-tion errors for both methods we observe that both methodswere able to reconstruct a natural grasp with minimal errorhowever ULDA was unable to replicate joint extension inthe thumb and pinky PIP joints Figure 7 (bottom) shows areconstruction of a natural grasping task number 75 whichhad the highest reconstruction error for both methods Inthis task the recorded movement (red) lacks smooth velocitypatterns and is also characterized by lower velocities Thistype of movement was also seen in natural grasping tasksnumbered 1 12 17 18 38 49 and 80 Both methods wereunable to replicate this type of movement although PCAhad lower errors Reconstruction errors of ASL posturalmovements were greater than those of natural grasps forboth methods Figure 7 (top) shows the best reconstructionof an ASL postural movement (task number 29) PCA wasunable to replicate themagnitude of velocitywhileULDAwasunable replicate the temporal structure of each joint angularvelocity profile ASL postural movement task number 9 hadthe highest reconstruction error and is shown in Figure 8(bottom) Both methods were unable to replicate extensionthat was not consistent across joint types

4 Discussion

Anatomical neural and functional coupling in the humanhand suggests that all possible hand postures from everydayactivities lie in a lower-dimensional subspace that can becharacterized by kinematic synergies [5] The synergies inthis paper were derived from grasping kinematic data andwere tested for generalizability on ASL postures Principalcomponent analysis was performed on the posture matrix orin otherwords on the high-dimensional space of 100 posturesmeaning the variables here are postures and the observationsare joint angular velocities for these postures The synergiesare principal components that are expressed as weightedlinear combinations of these 100 postures The weightsare derived from eigen vectors As principal componentsrepresent the axes aligned with the directions of maximumvariance the synergies are the most commonly found jointangular velocity patterns used during the 100 postural tasksSix synergies were found to account for 95 of the variance

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 5

parameter Thus the optimization problem solves for cyielding a sparse selection of synergies that minimizes thedifference between the recorded joint angular velocities of anatural grasping movement or ASL postural movement andjoint angular velocities of the reconstructed movement

To evaluate the reconstruction of natural and ASL postu-ral movements the reconstruction error was determined foreach task by

sum119899

119894=1sum119879

119905=1[V119892119894(119905) minus V119892

119894(119905)]2

sum119899

119894=1sum119879

119905=1V119892119894(119905)2

(14)

where V119892119894(119905) (119905 = 1 119879) is the angular velocity profile of

task 119892 and finger joint 119894 (119894 = 1 119899) reconstructed usinga given number of synergies This yields a ratio between theapproximate error and the original angular velocity profileThus an error of 1 represents a squared error of 1 at every timepoint and every task for each joint Presented results shownormalized error where an error of zero is minimum errorcorresponding to best reconstruction and an error of 1 is themaximum error corresponding to worst reconstruction

3 Results

PCA and ULDA described in Section 23 were used to derivekinematic synergies from preprocessed hand joint angularvelocities during rapid grasps The top six significant syner-gies derived from PCA and ULDA were used in reconstruc-tion of natural movements and ASL postural movementsFigure 2 shows a representative example of six synergiesderived from PCA and ULDA for one subject Synergies 1

and 2 derived from PCA show broad bell-shaped velocitypatterns while synergies 1ndash5 derived from ULDA especiallyin PIP joints show distinctly different patterns Interestinglysynergies derived from ULDA show an initial movementdelay which is consistent in PIP joints for synergies 1ndash5 Inboth methods velocity patterns for higher-order synergiesare characterized by multiple submovements Extension isfirst seen in synergy 2 derived from PCA and synergy 6derived from ULDA In terms of joint angular velocitypatterns kinematic synergies further reveal relationshipsfound between joints PIP joints reach a greater velocity thanMCP joints in synergies 1 and 3 Conversely MCP jointsreach a greater velocity than PIP joints in synergies 2 and4 The same inverse relationship where PIP joint reach agreater velocity thanMCP joints is found in synergy 1 derivedfrom ULDA However only synergy 5 shows a movementwhere MCP joints have greater velocities than PIP jointsThese results encourage further analysis on the importanceof each synergy In order to determine how the numberof synergies used in reconstruction affects performance ofeach method we calculated reconstruction errors for up to10 synergies (Figures 3 and 4) In both of these figures wecan see the performance of ULDA plateaus after 4 synergiesReconstruction error continues to decrease for PCA asmore synergies are used It is evident that PCA performsbetter than ULDA in natural grasp reconstruction Howeverreconstruction errors of ASL postural movements are similarfor both methods until 5 synergies are used after which

the performance of ULDA plateaus and PCA error decreases(Figure 4)

Using the optimization algorithm all natural grasps andASL postural movements were reconstructed Figure 5 showsthe mean reconstruction errors for 100 natural movementsacross 10 subjects Error bars indicate the standard deviationacross 10 subjects Similarly Figure 6 shows the mean recon-struction errors for 36 ASL postural movements Error barsindicate the standard deviations across 10 subjects PCA hadthe best overall performancewithmean reconstruction errorsof 008 and 02002 for natural grasping and ASL posturalmovements respectively ULDA has reconstruction error of01867 and 03147 for natural grasping and ASL posturalmovements respectively Green and red arrows indicatemovements that had the best and worst reconstructions forboth methods respectively These reconstructions are shownin Figures 7 and 8 Figure 7 (top) shows a reconstruction ofgrasping task number 47 which had the lowest reconstruc-tion errors for both methods we observe that both methodswere able to reconstruct a natural grasp with minimal errorhowever ULDA was unable to replicate joint extension inthe thumb and pinky PIP joints Figure 7 (bottom) shows areconstruction of a natural grasping task number 75 whichhad the highest reconstruction error for both methods Inthis task the recorded movement (red) lacks smooth velocitypatterns and is also characterized by lower velocities Thistype of movement was also seen in natural grasping tasksnumbered 1 12 17 18 38 49 and 80 Both methods wereunable to replicate this type of movement although PCAhad lower errors Reconstruction errors of ASL posturalmovements were greater than those of natural grasps forboth methods Figure 7 (top) shows the best reconstructionof an ASL postural movement (task number 29) PCA wasunable to replicate themagnitude of velocitywhileULDAwasunable replicate the temporal structure of each joint angularvelocity profile ASL postural movement task number 9 hadthe highest reconstruction error and is shown in Figure 8(bottom) Both methods were unable to replicate extensionthat was not consistent across joint types

4 Discussion

Anatomical neural and functional coupling in the humanhand suggests that all possible hand postures from everydayactivities lie in a lower-dimensional subspace that can becharacterized by kinematic synergies [5] The synergies inthis paper were derived from grasping kinematic data andwere tested for generalizability on ASL postures Principalcomponent analysis was performed on the posture matrix orin otherwords on the high-dimensional space of 100 posturesmeaning the variables here are postures and the observationsare joint angular velocities for these postures The synergiesare principal components that are expressed as weightedlinear combinations of these 100 postures The weightsare derived from eigen vectors As principal componentsrepresent the axes aligned with the directions of maximumvariance the synergies are the most commonly found jointangular velocity patterns used during the 100 postural tasksSix synergies were found to account for 95 of the variance

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Samples Samples Samples

SamplesSamplesSamples

Synergy 1 Synergy 2 Synergy 3

Synergy 5 Synergy 6

0 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0010

minus0010

minus002

002

0minus002

0020

minus002

002

0minus002

002

005

0minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

minus005

0050

0

0

0

minus005

0050

minus005

02

0

minus02

020

minus02

020

minus02

020

minus02

020

minus02

02

0

minus02

02

0

0

minus02

02

0minus02

020

minus02

020

minus02

020

minus02

020

minus02

020

minus02

01

01

02

02

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

001

minus01

01

minus01

001

minus01

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

002

minus02

Synergy 4

T-MCP

T-MCP

Figure 2 Six kinematic synergies obtained for subject 2 using PCA (red) and ULDA (green) Each synergy is about 045 s (39 samples) induration (data acquired at 86Hz) T thumb I index finger M middle finger R ring finger P pinky finger MCP metacarpophalangealjoint IP interphalangeal joint PIP proximal IP joint

Linear discriminants on the other hand as candidates for syn-ergies represent postures that stand distinct among groups in100 postures The groups were formed based on the nearestneighbors computed by measuring the Euclidian distancesbetween postures

Results show that PCA outperforms ULDA in recon-struction of natural grasping movements and ASL posturalmovements Does that mean that PCs are optimal low-dimensional representations of hand movements andhence ideal candidates for synergies Linear discriminants

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 7

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 3 Mean reconstruction errors for PCA (blue) and ULDA(red) using up to 10 synergies are shown Reconstruction errors fornatural grasping movements were less for PCA derived synergiesthan ULDA derived synergies Reconstruction errors for ULDAplateaued after 5 synergies

PCAULDA

05

04

03

02

01

0

0 2 4 6 8 10 12

Number of synergies recruited

Nor

mal

ized

reco

nstr

uctio

n er

ror

Figure 4 Reconstruction errors for ASL postural movements weresimilar for both PCA and ULDA up to 5 synergies after whichULDA errors plateaued and PCA errors decreased

although representing the six most distinct joint angularmovement velocity patterns may not be ideal candidatesfor synergies as they are not capturing the commonlyfound joint angular velocity patterns Interestingly previousstudies exploring muscle synergies have found distinctpatterns through clustering to be more effective thanPCA in synergy extraction Krouchev et al [19] foundthat distinct muscle groups characterize each synergyextracted from cat locomotion movements via associative

PCA

ULD

A

1

05

0

1

05

0

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Natural grasps

Natural grasps

Figure 5 The mean reconstruction errors for 100 natural grasp-ing movements using PCA and ULDA across all subjects PCAperformed better than ULDA Reconstruction error is computedby (14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 7

ASL postures

ULD

APC

A

1

05

0

1

05

0

5 10 15 20 25 30 35

ASL postures5 10 15 20 25 30 35

Figure 6 The mean reconstruction errors for 36 ASL posturalmovements using PCA and ULDA across all subjects PCA per-formed better than ULDA Reconstruction error is computed by(14) Two tasks corresponding to best and worst reconstructionerrors were indicated by green and red arrows respectively Thesewere further illustrated in Figure 8

clustering Ajiboye andWeir [13] using NMF also found thatpopulation synergies extracted from hand movements (ASLpostures) were dominated by a single muscle while subject-specific synergies involved coactivation of multiple musclesAlthough in muscle space distinct groups of muscles maybetter characterize movement this phenomenon does notcarry to kinematic space PIP joint angular velocities showeda distinct waveform that could be seen in synergies 1ndash5extracted from ULDA while the 6th synergy shows a similarjoint angular velocity profile across all PIP and MCP jointsULDA failed to capture the relationship between allMCP andPIP joints in multiple synergies as indicated in the synergypatterns (Figure 2) Natural coupling between fingers as aresult of single or multiple muscle activations is captured

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Computational Intelligence and Neuroscience

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples Samples

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

PCA ULDA

PCA ULDABest reconstruction example of a natural grasp

Poor construction example of a natural grasp

002

0

002

0

minus002minus002

005

0

minus005

005

0

minus005minus005

minus010

minus010

minus010

0minus01

0

minus010

minus01

minus01

0

minus010

minus010

minus010

minus010

minus010

minus010

minus01

minus01

0

0

001

0

minus001

0010

minus001

002

0 0

minus002

002

0

minus002

002

minus002

0

002

minus002

0

002

minus002

minus002

0

002

minus002

005

0

minus005

005

0

minus005

005

0minus005

005

0

minus005

005

0

minus005

005

0

0 0

0minus005

005

minus005

0

005

minus005005

minus005

005

0

minus005

0050

minus005

minus004

01

01

01

01

01

01

01

01

01

01

01

01

01

01

01

0

minus01

T-MCP

T-MCP

Figure 7 Top the lowest reconstruction error for both methods in natural grasping movement reconstruction was found in grasping tasknumber 47 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found ingrasping task number 75 Its reconstruction is shown using PCA and ULDA T thumb I index finger M middle finger R ring finger Ppinky finger MCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

by both PCA in synergies 1ndash4 and ULDA in synergies 1ndash6because all 4 fingers MCP show similar velocity patternsSynergies 5 and 6 derived from PCA however do notrepresent physiological couplings but may characterize lesscommonly used and more independent movements during

grasping For example synergy 5 derived from PCA showsR-PIP extension during M-PIP flexion which does not seemintuitive but may be a result of more complex grasps

Although PCA derived synergies outperform ULDAderived synergies in ASL postural movement reconstruction

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 9

minus002

minus002

minus005

minus005

minus005

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80

Samples

Samples

Samples

Samples

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

P-PIP

P-MCP

R-PIP

R-MCP

M-PIP

M-MCP

I-PIP

I-MCP

T-IP

PCA

PCA

ULDA

ULDA

002

0

minus002 minus002

002

0

minus002

minus002

002

0

minus002

005

0

0

0

minus005 minus005

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

0

02

minus02

02

minus02

0

02

minus02

002

0

005

0

0

0

minus01

0

minus01

minus01

02

minus02

0

0

minus010

0

02

minus02

02

minus02

0

02

minus02

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

005

0

minus005

002

0

002

0

minus002

002

0

002

0

0

02

minus02

005

0

005

0

005

0

minus005

005

0

minus005

005

0

Poor reconstruction example of an ASL posture

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Ang

ular

vel

ociti

es o

f ten

join

ts (r

adia

nss

ampl

e)

Best reconstruction example of an ASL posture

01

01

0101

01

01

01 01

T-MCP

T-MCP

Figure 8 Top the lowest reconstruction error for both methods in ASL postural movement reconstruction was found in ASL postural tasknumber 29 Its reconstruction is shown using PCA and ULDA Bottom the highest reconstruction error for both methods was found in ASLtask number 9 Its reconstruction is shown using PCA and ULDA Tthumb I index finger M middle finger R ring finger P pinky fingerMCP metacarpophalangeal joint IP interphalangeal joint PIP proximal IP joint

there is still an increase in error for both during reconstruc-tion of ASL postural movements One possible source forincreased error in ASL reconstruction is that ASL posturesrequire extreme decoupling of fingers For example thethree distal fingers are anatomically coupled and grasping

movements do not usually force them apart However inASL number 8 (task number 9) requires the subject toflex the middle finger with the assist of the thumb whileconsciously trying to extend the ring finger Since the middleand ring fingers are naturally coupled synergies are unable

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Computational Intelligence and Neuroscience

to capture such an extreme movement resulting in highestreconstruction error (Figure 6)

In summary two contrasting dimensionality reductionmethods PCA that maximizes variance and LDA thatdiscriminates variance have been used to extract synergiesThe contribution of linear discriminants plateaued beyond5 synergies but the contribution of principal componentscontinued beyond six synergies PCA outperformed LDAin reconstruction of natural grasping and ASL posturalmovements The shape smoothness and representations ofnatural joint couplings found in joint angular velocity profilesmay have contributed to differences in reconstruction errorsCertain types of natural grasps namely those characterizedby irregular and noisy velocity profiles yielded higher recon-struction errors for both methods ASL postural movementsincluded unnatural flexion and extension of fingers that arenot involved in the activities of daily living For this reasonboth PCA and LDA had greater errors in reconstruction ofASL movements In the future combinations of linear andnonlinear dimensionality reduction methods will be used inreducing the dimensionality of hand movement kinematics

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Science Foundation(NSF) underGrant CMMI-0727256 andNational Institute onDisability and Rehabilitation Research (NIDRR) under GrantH133F100001

References

[1] N BernsteinThe Co-Ordination and Regulation of MovementsPergamon Press Oxford UK 1967

[2] M C Tresch P Saltiel and E Bizzi ldquoThe construction ofmovement by the spinal cordrdquo Nature Neuroscience vol 2 no2 pp 162ndash167 1999

[3] R Vinjamuri D J Weber Z H Mao et al ldquoToward synergy-based brain-machine interfacesrdquo IEEETransactions on Informa-tion Technology in Biomedicine vol 15 no 5 pp 726ndash736 2011

[4] C L Mackenzie and T Iberall The Grasping Hand Advancesin Psychology North-Holland Publishing Amsterdam TheNetherlands 1994

[5] J N Ingram K P Kording I S Howard and D M WolpertldquoThe statistics of natural hand movementsrdquo Experimental BrainResearch vol 188 no 2 pp 223ndash236 2008

[6] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-HMao ldquoDimensionality reduction in control and coor-dination of the human handrdquo IEEE Transactions on BiomedicalEngineering vol 57 no 2 pp 284ndash295 2010

[7] M Popovic and D Popovic ldquoCloning biological synergiesimproves control of elbow neuroprosthesesrdquo IEEE EngineeringinMedicine and BiologyMagazine vol 20 no 1 pp 74ndash81 2001

[8] S D Iftime L L Egsgaard and M B Popovic ldquoAutomaticdetermination of synergies by radial basis function artificial

neural networks for the control of a neural prosthesisrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 13 no 4 pp 482ndash489 2005

[9] J Romero T Feix H Kjellstrom and D Kragic ldquoSpatio-temporal modeling of grasping actionsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2103ndash2108 October 2010

[10] I Havoutis and S Ramamoorthy ldquoConstrained geodesic tra-jectory generation on learnt skill manifoldsrdquo in Proceedings ofthe 23rd IEEERSJ 2010 International Conference on IntelligentRobots and Systems (IROS rsquo10) pp 2670ndash2675 October 2010

[11] R H Clewley J M Guckenheimer and F J Valero-CuevasldquoEstimating effective degrees of freedom in motor systemsrdquoIEEE Transactions on Biomedical Engineering vol 55 no 2 pp430ndash442 2008

[12] A DrsquoAvella P Saltiel and E Bizzi ldquoCombinations of musclesynergies in the construction of a natural motor behaviorrdquoNature Neuroscience vol 6 no 3 pp 300ndash308 2003

[13] A B Ajiboye and R F Weir ldquoMuscle synergies as a predictiveframework for the EMGpatterns of new hand posturesrdquo Journalof Neural Engineering vol 6 no 3 Article ID 036004 2009

[14] C R Mason J E Gomez and T J Ebner ldquoHand synergiesduring reach-to-grasprdquo Journal of Neurophysiology vol 86 no6 pp 2896ndash2910 2001

[15] M Santello M Flanders and J F Soechting ldquoPatterns of handmotion during grasping and the influence of sensory guidancerdquoThe Journal of Neuroscience vol 22 no 4 pp 1426ndash1435 2002

[16] P H Thakur A J Bastian and S S Hsiao ldquoMultidigit move-ment synergies of the human hand in an unconstrained hapticexploration taskrdquoThe Journal of Neuroscience vol 28 no 6 pp1271ndash1281 2008

[17] R Vinjamuri M Sun C-C Chang H-N Lee R J Sclabassiand Z-H Mao ldquoTemporal postural synergies of the handin rapid grasping tasksrdquo IEEE Transactions on InformationTechnology and Biomedicine vol 14 no 4 pp 986ndash994 2010

[18] M C Tresch V C K Cheung and A drsquoAvella ldquoMatrix fac-torization algorithms for the identification of muscle synergiesevaluation on simulated and experimental data setsrdquo Journal ofNeurophysiology vol 95 no 4 pp 2199ndash2212 2006

[19] N Krouchev J F Kalaska and T Drew ldquoSequential activationof muscle synergies during locomotion in the intact cat asrevealed by cluster analysis and direct decompositionrdquo Journalof Neurophysiology vol 96 no 4 pp 1991ndash2010 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014