Analysis and Visualization of Movement related EEGactivities using Local Discriminant Bases

N.Fırat İnce, Ahmed Tewfik*, Sami Arıca, Suha Yağcıoğlu **University of Cukurova

Department of Electrical and Electronics Engineering, Adana, Turkey*University of Minnesota

Department of Electrical Engineering, MN, USA**University of Hacettepe

Department of Biophysics, Ankara, Turkey

Abstract- We use local cosine packets to adaptively segment EEGcorresponding to left or right hand index finger movements. Thesegmentation is constructed by maximizing the Euclidean orKullback-Leibler distance criterion between the left and rightfinger movement. The proposed method divides the movementEEG from the C3 and C4 electrodes into nonuniform timesegments over a dyadic tree. The most discriminative featuresare selected from the pruned tree. We observed that the selectedsegmentation and discriminative components are subjectspecific. We believe this may eliminate the inter and intra-subject variability when constructing Brain ComputerInterfaces. We also found striking asymmetry between featurecharacteristics and their discrimination power on eachhemisphere.

I. INTRODUCTION

It is well known that an event can induce rhythmicpatterns in EEG like amplitude attenuation and increase.These activities are called event-related synchronization(ERS) and desynchronization (ERD) respectively [1].Movement and its imagination are such events and can induceERD and ERS in the motor cortex. It has also been shownthat movement imagery related rhythmic activities could beused to construct brain computer interfaces [2]. For thisreason investigation of ERD and ERS due to voluntarymovement has gained significant interest. Several methodswere proposed to quantify and visualize ERD and ERS. Bandpass filtering (BPF) and auto regressive (AR) modeling arethe most common ones [3,4]. BPF requires prior knowledgeof reactive bands. The reactive bands are detected bycomparing the reference interval spectrum with an activesegment spectrum. Frequency bands, that show significantchange, are selected by the filtering process. It is assumed thatthe selected interval is an active segment. On the other hand,it is well known that the time and frequency characteristics ofthe alpha and beta components can vary widely [5,6]. Theselection of the active segment can therefore be a problem iffixed windows are used. Auto regressive modeling attemptsto overcome this problem using parameters that define thedynamic spectral information. In general, the signal issegmented into short intervals where local stationary isassumed. In addition to BPF and AR modeling, localtrigonometric bases were used to adaptively segment themovement EEG [7]. In this case, adaptive windows are

automatically adjusted to represent the underlying time-varying signal spectrum.

In order to construct brain computer interfaces, one needsto know the most relevant bands for classification. Distinctionsensitive learning vector quantization (DSLVQ) was used toselect relevant bands in fix segments [8]. This method tries toperfectly adapt the bands for discrimination. However, ERSand ERD do not necessarily occur in a specific given timeinterval. This method ignores the possibility that subjects mayhave physio-anatomical differences and/or different imagerystrategies to induce ERD and ERS patterns. In [9] adaptiveautoregressive (AAR) modeling is used to select the best timepoint for classification. Since AAR parameters define thespectrum dynamically, they adapt to band power or subjectspecific frequency patterns. Both DSLVQ and AARparameters show that subject specific time and frequencydomain EEG signal features do exist.

Recently we have shown that movement induced EEGsignals can be analyzed and classified using adapted bases[10]. In this paper, we visualize, analyze and interpret theclassification features selected by our procedure when it isapplied to EEG signals corresponding to left or right handindex finger movements.

II. MATERIALS AND METHODS

A. Cosine Packets

Short time Fourier transforms is traditionally used toanalyze the local frequency content of a signal. This type ofblock transform generates side-lobe artifacts when disjointrectangular windows are used. When smooth windows areused, orthogonality is lost. It is possible to constructorthogonal transforms with smooth and overlapping windowsby using trigonometric bases. The construction can beobtained from sine or cosine bases. The cosine packetcoefficients can be computed with fast discrete cosinetransform (type IV), after a preliminary folding step [11].Here we select local cosine packets, which are the timecounterpart of Wavelet Packets. They partition the time axisrather than the frequency axis. We also believe that thestructure of Cosine Packets (CP) is suitable to analyze timelocked oscillatory signals.

B. Local Discriminant Bases

Important features for classification often appear as atransient phenomenon. For this reason it is important to focuson local properties of the signal. The best basis algorithm wasdeveloped to extract such local information [12]. However themain concern of this method is signal representation. Thismethod expands the signal into orthonormal bases by usingwavelet packets or local trigonometric bases over a dyadicgrid – binary tree. This full tree is then pruned to minimize acost function, such as entropy, by a divide and conqueralgorithm. If the selected cost function is entropy, such analgorithm ends up selecting the sub basis, which maximizessignal compression. For classification, the discriminationpower of the nodes must be measured. Therefore, the entropycriterion is replaced by another cost function, which canmeasure the distance of the nodes between the classes. Bypruning the binary tree to maximize the selected costfunction, local discriminant bases (LDB) are extracted [13].

There are various choices for distance measures. Assume,p q are normalized energy distributions of signals belonging

to class1 and class2 respectively. We have used:• The symmetric Kullback Leibler distance, which is also

named as J-divergence,

1

( , ) logn

ii

i i

pI p q p

q=

= ∑ (1)

( ) ( )( , ) , ,J p q I p q I q p= + (2)• Euclidean distance

( ) ( )2 2

1

,n

i i i ii

D p q p q p q=

= − = −∑ (3)

We also considered the Fisher class separability criterion forfeature selection.

( )1 2

2 2

1 2

Fµ µ

σ σ

−=

+ (4)

where µ and σ are the mean and standard deviation of thefeature it belong to. We shall refer to the Kullback Leibler,Euclidean and Fisher criteria as the J, D and K distancecriteria respectively.

C. Experimental Data

The movement EEG data was collected from threevolunteers (S1, S2 and S3). Consecutive movements of fingerwere performed not shorter than 10 sec. And they weredetected via a micro-switch. EEG was digitized from 19electrodes selected from the extended 10-20 system withNuamps Neuroscan™. The electrode skin impedance waskept below 10 kΩ. The signal was sampled with 250 Hz.Channels on motor cortex were transformed into localaverage derivation.

D. Feature Extraction and Segmentation

Since the C3 and C4 electrodes are the most activeelectrodes in a hand/finger movement task, we construct twoadaptive segmentations; one for C3 and the other for C4

electrodes, in order to maximize the distance between left andright events. After the segmentation, we find the averagepower of the frequency bands (1-4; 5-8; 9-12; 13-16; 17-20;21-24; 25-32; 33-40 Hz) in each segment and sort thecoefficients from the time frequency plane according to theirdiscriminating power (DP). Then we select the top N featuresfrom each channel for visualization. We typically select N inthe range of 16 to 24 because most of the DP is concentratedin these coefficients (See Fig1.). This can be seen as anautomated feature reduction method, where similarapproaches were used in denoising via Wavelet Packets [14].

III. RESULTS

A. Time Segmentation

For three subjects the adaptive time segmentation wasconstructed using Local Cosine Packets. The dyadic tree waspruned by maximizing the J and D distance criteria. Inorder to see whether the segmentation is random or robust wedivided the dataset into two random groups and constructedthe segmentation for each subgroup. We repeated thisprocedure twice. We observed that the selected subtreesometimes changes depending on the dataset. We believe thatthe noise level in each data or small differences between theinformation captured by a mother node and its children in thetree can cause such instability. Therefore, we pruned the treeusing the following rule.

1 2( ) ,

,

.

mother child childIf d d d

keep mother

else

keep children

ϕ>= + ×

where id is the discrimination power of the node i ? of thedyadic tree and ϕ is an empirically selected constant. Wefound experimentally that 0.95ϕ = preserves discriminativeinformation while leading to robust segmentation. As a resultwe keep the mother if it captures 95% of the discriminativeinformation of the children, otherwise we keep the children.After this update we did not observe any important changedepending on the dataset. Since both the J and D criteriaresulted in similar sub-trees, we visualize the J basedinformation in the following figures for three subjects. As canbe seen in Fig. 2, the algorithm constructed different tilingsfor each channel and for each subject.

B. Time-Frequency Patterns

According to the algorithm, it was seen that not only thetime segmentation obtained but also the selected features aresubject depended. We also observed that the topdiscriminative features come from different time locations(Fig.3.). With the J or D distance functions, mostdiscriminative components are located in pre and postmovement alpha-beta bands. When the feature selectioncriterion is replaced with the F criterion, then the coefficients

with most discriminating power move to post movement betasynchronization. Furthermore, for subject S1 a widefrequency range is selected during the movement. The maincharacteristic of this region is the low amplitude of the EEGsignal where it corresponds to ERD. This is due to the factthat the Fisher ( F ) criterion does not take only the distancebetween the means into consideration but also the variancedistributions as well. As a result, features with large variancesare pushed back in the sorted coefficient queue. Since thealpha components have large variances, their relativediscriminant power is reduced when the F criterion is used.

We also noticed the asymmetry between C3 and C4features. For subjects 2 and 3 the DP of C4 is radically greaterthan C3’s. Independent of the side of the finger, the lefthemisphere is always involved in producing the movement.The right hemisphere seems to be involved only when thesubject executes a left-hand finger movement.

IV. CONCLUSION

We used local discriminant bases obtained from localcosine packets to select the most discriminative componentsof an EEG signal corresponding to left or right hand indexfinger movements. The features are selected from an adaptivetime segmentation of the EEG signal from C3 and C4electrodes. The coefficients with the most discriminatingpower were located in the alpha and beta bands, justifying thealmost universal selection of these two EEG bands for basicresearch on cortical mechanisms of movement as well as inefforts towards a brain computer interface. When theKullback Leibler or Euclidean distance criteria is used forfeature selection, the alpha components are selected as theprimary discriminant features. Interestingly, except forSubject1, no or minimal, features are selected in the ERDregion where the movement is executed. When Fishercriterion is used, the top coefficients are always located onpost movement components. Especially for Subject2 andSubject3 the beta ERS is selected as the primary feature.Various authors reported that the beta ERS is more correlatedwith the movement variables and hand dominance. This maybe a reason why they are selected. We also notice that for S1some features are selected in beta band right after themovement, which agrees with the burst activity characteristicof that component [6]. These features are detected in a verysmall interval right after the movement. This explains whyadaptive algorithms are suitable to capture such temporalactivities [7,10]. The algorithm constructed differentsegmentations for each subject as should be expected fromthe well-known inter-subject variability of EEG. Also weobserved an asymmetry between the hemispheres whichwould suggest a more comprehensive systematic study inwhich hand preference and hemispheric dominance of thesubjects could be taken into account. This finding alsocorrelates with a recent study where the asymmetry of twohemispheres is modeled with a Hidden Markov Model and agenetic algorithm. The authors reported a significantimprovement when such an asymmetric classifier is used forclassification [15].

Fig. 1. The normalized cumulative distance of channels C3 and C4 forsubjects S1,S2 and S3. Note that nearly %90 percent of discrimination poweris concentrated on the first 30-50 features for all subjects.

(a)

(b)

(c)

Fig. 2. Adaptive dyadic tilings (a), (b) and (c) for the subjects S1, S2 and S3respectively. The discriminitive criteria is J

ACKNOWLEDGMENT

This project is supported by The National Scientific ResearchCouncil of Turkey (TUBITAK). Project No. 103E030

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Subject1

Subject2

Subject3

(a) (b)

Fig. 3. Discriminative T-F maps (Time segmentation criterion is J ). (a) The feature selection criterion is J . (b) The feature selection criterion is F .Notice that changing the feature selection criteria effects the order of coefficients. Especially alpha components lose their rank. The arrow indicates theonset of the self-paced finger movement.