TransferLearningandIdentificationMethodofCross-ViewTarget … · 2020. 12. 24. · 4.2.AnalysisofExperimentalResults. eﬁrstexperiment aimstoqualitativelycomparetheperformanceoftheHMM

Research ArticleTransferLearningandIdentificationMethodofCross-ViewTargetTrajectory Utilizing HMM

Long Liu Le Yang and Jie Ding

e Faculty of Automation and Information Engineering Xirsquoan University of Technology Xirsquoan 710048 China

Correspondence should be addressed to Long Liu liulongxauteducn

Received 2 October 2020 Revised 16 November 2020 Accepted 9 December 2020 Published 24 December 2020

Academic Editor Hussein Abulkasim

Copyright copy 2020 Long Liu et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

)e behavior identification of the target trajectory is one of the important issues in space behavior analysis Since the targettrajectory model obtained from a fixed view cannot be adapted to the change of the observation perspective it needs to beretrained when being faced with a new view which leads to a great amount of increment in application cost)is study proposes ahidden Markov model (HMM) based on the cross-view transfer learning and the recognition method that firstly constructs alinear mapping relationship between the observation matrices of the source and target view utilizing the domain trajectory of theHMMs and obtains the observation matrix parameters of the target domain through the mapping system Secondly the transferprobability of the source domain is further optimized to obtain the target domain of the HMM and to identify the behavior of thetarget domain trajectory utilizing a small number of samples from the view of the target domain )e experimental results denotethat the proposed method could effectively realize the identification of the trajectory behavior utilizing a small sample size in thetarget domain and would greatly reduce the application cost of the identification of the cross-view target trajectory

1 Introduction

Target trajectories reveal important information on targetbehavior and the identification of the trajectory is animportant part pertinent to understanding an event andbehavior analysis In real applications a video surveillancesystem often composes of multiple cameras located atdifferent angles )e motion trajectory of the same target isdisplayed differently from diverse perspectives )etraining of the trajectory model relies on samples from afixed perspective When the perspective alters new samplesneed to be collected and retrained leading to the exces-sively high training cost for the trajectory model whichwould greatly raise the application cost of the identificationof the trajectory behavior )is is not conducive to itspromotion Pointing out that it has a high application valueand practical importance to research on the behavioridentification method of the low-cost cross-view targettrajectory

Hidden Markov model (HMM) [1ndash8] could effectivelymodel time-series signals and is a powerful tool to model the

target tracking Qiming and Cheng propose that trajectorymodeling is executed according to the trajectory coordinatesequence [1] In this method the trajectory sequence is firstlyclustered and then the corresponding HMM trajectorymodel is attained utilizing the training of the diverse cate-gories Dapeng et al suggest that the HMM is utilized tomodel the trajectory of the enemy submarine and to predictthe trajectory of the target to provide operational infor-mation support for warship operations [2] Hervieu et alpropose that the curvature and velocity of the coordinatepoints are utilized for the HMM trajectory modeling and thetrajectory characteristics are invariant to translation rota-tion and scaling [3] Qian and Lau suggest that a layeredHMM is proposed to model the continuous target trajectoryin a multilayer scene that leads to both a low-level HMM tomodel the single-layer trajectory and a high-level HMMconnecting the multilayer trajectory to form the targettrajectory model [4]

On the other hand transfer learning has graduallybecome an important research area in machine learning inrecent years since it mainly has resolved the problem

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 6656222 13 pageshttpsdoiorg10115520206656222

related to the learning of the cross-domain knowledge andcould realize the model migration when the data of thetarget domain is unlabeled and the data of the sourcedomain is called a multisource Moreover it has a hightheoretical value in many practical problems Transferlearning which relaxes two basic assumptions in tradi-tional machine learning is a new method in the field ofmachine learning Its main characteristics could besummarized as follows (1) there must be enough samplesto learn for a good classification model (2) Both thetraining samples were utilized for learning and the newtest samples meet the conditions of independence andidentical distribution properties Some scholars haveproposed various HMM transfer methods for some cross-domain applications For instance Van Kasteren et alpropose that a parameter transfer learning method utilizesthe HMM that constructs the sensor mapping relationshipaccording to the location information of the spatialstructure and then finds out the parameters of the HMMutilizing the EM algorithm [9] Zheng et al propose that ittakes the received real-time signal intensity of mobiledevices as the observed value to construct the HMMpositioning model and realizes the transfer of it at dif-ferent times in the same position [10] Bingtao et alsuggest that giving weight to the sample data of the sourcedomain by calculating the similarity between the sourcedomain and the target domain sample data then finds outthe HMM parameters in the weighted data set and im-proves the learning algorithm to realize the instance-based HMM transfer learning [11] Similar researchstudies conducted by Kim et al propose that an HMMtransfer method utilizing the maximum a posterior(MAP) and maximum likelihood linear regression(MLLR) is applied to speech and text recognition [12ndash15]Some empirical research studies related to HMM are Feiet al in [16 17]

As a contribution to this research area to solve the low-cost application problem of the HMM trying to determinethe trajectory behavior in different perspectives this man-uscript proposes an HMM-based transfer learning andrecognition method for the behavior of the target trajectorywhere the cases consist of the perspective samples of thesufficient source domain and the perspective samples of fewmarked target domain exist )is method achieves thepurpose of transfer learning and recognition by transferringthe trajectory behavior model in the source perspectivedomain and optimizing a small number of samples in thetarget domain which provides an effective way to resolve thementioned problem

2 The Proposed Model Trajectory Modelingand Simulation

21 Target Trajectory Model Based on the HMM HiddenMarkov model (HMM) is a probabilistic model describingthe process of time series which can be described by fivecomponents denoted by a quintupleλ (N M A B and π) Moreover its simplified form isrepresented by λ (A B and π)

(1) N indicates the number of hidden states in themodel All states in the model are interconnectedand any state can be reached from other states

(2) M represents the observation symbol of each hiddenstate in the model ie the number of observationstates

(3) A is called the probability distribution of state tran-sition A aij1113966 1113967 where aij p(Qt+1 j|Qt i)0le aij le 1 and 1113936

Ni1 aij 1 1le i jleM Qt is called

the hidden state at time t(4) B is called the probability distribution of the observable

state in the hidden state at moment j B bik1113864 1113865 wherebik p(Qt k|Qt i) and 1le ileN 0le kleM Qt iscalled the observable state at time t

(5) π is called the distribution of the initial state π πi1113864 1113865where πi p(Q0 i) 1le ileN

According to the basic definition of the HMM thismanuscript firstly conducts the HMM modeling for thetarget trajectory )e direction angle of the trajectory of thetarget in a unit of time is utilized as the observation char-acteristic )e sequence of the angle representing the tra-jectory information is called the observable state vector )ehidden state is called the transfer characteristic of the anglechange of the target trajectory )e angular direction of thetarget trajectory is computed by

φt tanminus1 yt minus ytminus1

xt minus xtminus11113888 1113889 (1)

where (xt yt) and (xtminus1 ytminus1) are called the target positionsat time t and tminus 1 respectively According to φt the observedvalue Qt is attained by discretizing the 24-direction freemancode depicted in Figure 1)e parameters of the trajectory ofthe HMM are obtained by training

)e trajectory presented in Figure 2 is utilized formodeling )e coordinate sequence of the target trajectory ispresented in Table 1)e angle characteristic is computed by(1) and its discretization is presented in Table 2 While thenumber of the hidden states called N is set to 4 that ofobservation called M is set to 24 )e probability vector ofthe initial state denoted by π is defined as uniform distri-bution )e transfer probability and the probability distri-butions of the observation are initialized randomly )etrajectory samples above are trained by the BaumndashWelchalgorithm to attain the parameters of the initial distributionπ transfer probability matrix A and observation probabilitymatrix B respectively that are presented in Table 3

22 Simulation of the Target Trajectory )ere are two im-portant assumptions in the HMM which are expressed asfollows (1) homogeneous Markov Chain hypothesis that isthe hidden state at any time only depends on its previoushidden state (2) Observation independence hypothesis thatis the observed state at any time only depends on the hiddenstate at the current time

As presented in Figure 3 the hidden Markov Chainbased on the above hypothesis is determined by the initial

2 Mathematical Problems in Engineering

state probability vector and the state transfer probabilitymatrix A Hence the result of which is to generate an un-observable hidden state sequence )e observation proba-bility matrix B and the hidden state sequence are combinedto determine the way of generating an observable sequence

Given the HMM model in the form ofλ (N M A B and π) the observation sequenceO O1 O2 OT could be generated by the algorithmsteps presented in Table 4 According to the initial coor-dinates of the trajectory and the sequence of the observedvalues the coordinates of the trajectory sequence could beuniquely determined

)e trajectory of the HMM is trained and simulatedunder four different circumstances and the results arepresented in Figure 4

23 Statistical Analysis of the Trajectory Characteristics fromDifferent Perspectives To further analyze the relationshipbetween the characteristics of the target trajectory fromdiverse perspectives this manuscript utilizes both a straightline and curve trajectories as illustrative examples to ex-amine their statistical characteristics of the observationcharacteristics from diverse perspectives When the targetlinear trajectory is a concern Figure 5 denotes the obser-vation of the linear motion of the same target from twodifferent perspectives )e statistical features of the char-acteristics of the target trajectory observation from twodifferent perspectives are presented in Figure 6 suggestingthat the statistical envelope of the trajectory characteristicsbetween the two perspectives is very similar while the centerof gravity is different

)e trajectory of the curve motion is presented in Fig-ure 7 Statistical analysis is conducted on the observationcharacteristics from different perspectives and the charac-teristic of the statistical curve is presented in Figure 8suggesting that the statistical characteristic of the curvedtrajectory from different perspectives have a certainsimilarity

To sum up although there exist differences in the per-spective a certain correlation exists in the performance ofthe feature sequence of the target trajectory If there weremore tracks along a certain direction they would accu-mulate near the characteristic coding of that directionHence it can be considered that the characteristic frequencycurves of the target trajectory from different perspectivesdenote a certain linear translation

3 Transfer Learning Based on the Trajectory ofthe HMM

For the recognition of the cross-view target trajectory smallsample data are employed in this research utilizing thetransfer learning strategy to obtain the trajectory of theHMM model for the target view and to realize the low-costmodeling of the behavior model of the cross-view trajectory)e basic idea of the HMM model based on the transferlearning in this manuscript is presented as follows firstlyaccording to the statistical translation of the trajectorycharacteristics in the different perspectives in Section 23 thelinear regression model is constructed to attain the mappingbetween the source domain and the target domain con-cerning the HMM observation probability matrices of thecharacteristics which leads to obtaining the observationprobability Secondly the transfer probability matrix israndomly initialized and the simulation data are generated)e objective optimization function is constructedaccording to the similarity between the simulation and thedomain data of the target Finally the parameters of thetransfer probability matrix for the trajectory HMM utilizingthe target domain are obtained through the iterative opti-mization and the transfer learning process of the cross-viewHMM is realized

Table 1 Centroid coordinate sequence of the target trajectory

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10X 280 278 275 272 270 269 266 262 258 252Y 155 157 160 169 169 170 173 177 182 189

1

2

34

56789

10

11

12

13

14

15

1617 18 19 20

2122

23

24

Figure 1 24-direction freeman code

(a) (b)

Figure 2 Target behavior trajectory (a) )e tracked target tra-jectory is overprinted on the background image (b) A sequence ofthe tracked target trajectories

Mathematical Problems in Engineering 3

Table 4 Algorithm of the simulation of the HMM to generate data

Algorithm steps of the simulation of the HMM to generate data(1) According to the initial state probability distribution π πi select an initial state Q1 i

(2) For t 1 2 3 K and TAccording to the output probability distribution bjk of state i output Qt kEND For

Markov chain(π A)

Random sequence(B)

State sequenceObservation

sequence

q1 q2 hellip qT o1 o2 hellip oT

Figure 3 )e simulation process of the HMM

Table 2 Direction freeman code of the target trajectory

i 2 3 4 5 6 7 8 9 10φi 0deg 135deg 1356deg 1616deg 900deg 1350deg 1350deg 1350deg 1413deg 1394degCode 10 10 11 7 10 10 10 10 10

Table 3 )e parameters of the HMM trajectory

π1 41 00000 00000 10000 00000A1 1 4 00024 09976 00000 00000A2 1 4 00000 00000 00536 09464A3 1 4 10000 00000 00000 00000A4 1 4 09044 00000 00956 00000B1 7 12 00000 00000 00000 09261 00000 00739B2 7 12 00000 00000 00000 07153 02831 00000B3 7 12 00000 00000 00000 07169 02831 00000B4 7 12 00835 01670 04174 00015 03306 00000

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(a)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(b)

Figure 4 Continued


31 Transfer of theObservation ProbabilityMatrix B )e keyto the transfer of the observation probability matrix is todetermine themapping relationship between the feature spacesof the target domain and the source domain By utilizing thismapping relationship to transfer the HMM parameters of thesource domain a parameter model is formed that can reflectthe target trajectory characteristics of the target domain

In this manuscript the least square method is adopted toconstruct the mapping model and the trajectory

characteristic of the mapping model under two differentperspectives is assumed to be represented by

Ot wOs + b (2)

where w and b are called the coefficients of a curve equationfitting by feature mapping Os is called a coding sample of thesource domain and Ot is called the coding data of the targetdomain after the mapping)e objective function is defined by

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(c)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(d)

Figure 4 Simulation data generated by the training model of the target trajectory from different views (from top to bottom are differentviews from left to right are the target trajectory samples and the results of the simulation generated by the training model)

(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)

Figure 5 )e position change of the linear trajectory of the same target in different perspectives (from top to bottom are the perspectives 1and 2 and from left to right are the frames 22 33 44 55 and 66)


(a) (b)

Figure 7 Position change of the curved trajectory of the same target under different perspectives (from top to bottom are called theperspectives 1 and 2 from left to right are called the positioning of the target under different perspectives and the trajectory of the targetunder different perspectives)

Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 23229 101112131415161718192021 240 7 8Direction chain code

Figure 8 Statistical frequency curves of the characteristics of the curve trajectory from different perspectives

Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700

76 8 95321 4 1011121314151617181920212223240Direction chain code

Figure 6 )e statistical frequency curves of the characteristics of the linear trajectory from different perspectives


1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)

where Ot is called the encoding data of the real targetdomain

According to the statistical analysis of the trajectorycharacteristics in Section 23 the transfer of the parameter ofthe observation probability mainly includes three stepsFirst both perspective trajectory samples of the sourcedomain and target domain are collected Each group ofsamples contains the source domain that is labeled as thesamples of the same behavior and as a small number of targetdomains that are labeled as the samples )e source domainof the HMM trajectory model denoted by λS (AS BS πS) isobtained according to the method of the training model inSection 21 )en the linear regression mapping modelabout source domain and target domain features is con-structed Finally the observation probability denoted by BTof the target domain is attained utilizing the relation transfermatrix BS of the linear regression

32 Transfer Learning Algorithm of the Transfer ProbabilityMatrix A Ignoring the effect of the initial distribution theinitial distribution πS of the source domain is directly mi-grated to the target domain to form πT and the transitionprobability of the source domain acts as the transitionprobability of the initial value 1113954AT of the target domain)enthe transferred initial HMM is denoted by 1113954λT (1113954AT BT πT)In this study the optimization algorithm is utilized toadaptively optimize the transfer of the model parameters toattain better performance of the target domain model )eparameters of the optimized target source model are moresuitable for the target domain data that is the more similarthe simulation data of the optimized model to the targetdomain data would be the better it would converge )eobjective function is defined by

minΔA

sim OT tOT1113960 1113961 sim g 1113954AT + ΔA BT πT1113872 1113873 OT1113960 1113961 (4)

where g(middot) is the mean value of the data generated by thesimulation λ(1113954AT + ΔA BT πT) and ΔA is called a variablein the optimization problem )e trajectory data is simu-lated according to the algorithm steps in Section 22 )einherent characteristics of the HMM require that thetransition matrix is non-negative and the sum of row el-ements is equal to 1 so the constraint conditions of thisoptimization problem are that the elements of the tran-sition probability matrix 1113954AT and 1113954AT + ΔA are non-negativeand the sum of row elements is equal to 1 )e measure-ment of similarity is determined by the Euclidean distancewhich is defined by

d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)

where OT and OTare the mean values of the feature sequenceset of the simulated trajectory model represented by 1113954λT

(1113954AT 1113954BT πT) and target domain respectively Hence both ofwhich belong to the same trajectory category )e similaritycomputation is defined by

sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)

Utilizing the constraints and objective function pre-sented above the interior point method is undoubtedly oneof the most suitable methods to resolve the optimal valueΔA Table 5 presents the steps of this solution procedureleading to the optimality of ΔA employing the interior pointmethod )e similarity between the simulated data of thetarget domain model and OT is calculated If the similarity isgreater than or equal to the similarity threshold denoted byδ the obtainedΔA from the previous optimization step is re-entered into the iteration of the interior point method as theinitial value until the computed similarity is less than thethreshold δ and then the HMM λT (1113954AT + ΔA BT πT)

(AT BT πT) of the target domain is attained

33 HMM Transfer Learning and Recognition FrameworkTo resolve the problem of the recognition of the cross-viewtarget trajectory this manuscript proposes a cross-viewHMM transfer method )e algorithm framework is pre-sented in Figure 9 Utilizing the objective function analysisthe statistics of the characteristics of the target trajectoryunder the two perspectives suggest a linear relationship)erefore the mapping function between the characteristicspaces of the source domain and the target domain is firstobtained by resolving an optimization problem based on thelinear regression model Utilizing the mapping function theparameters of the observation probability of the sourcedomain are transferred )en the similarity between thegenerated data of the simulated HMM and the labeled dataobtained from the target domain perspective is computed tofurther optimize the transition probability of the sourcedomain Hence the target domain HMM is obtained Fi-nally the forward algorithm is utilized to assess the matchclassification and identification of the cross-view targettrajectory

4 Experimental Results and Analysis

41 Experimental Evaluation )e data sets employed in thisexperiment are all self-collected data which come from thesimultaneous shooting of two cameras installed in the10times12m2 room )e 100 samples of three kinds of tra-jectories (300 in total) from view A of the first camera canbetter reflect the real movement behavior of the movingtarget )e 300 samples are taken as the source domain dataset while the corresponding 300 samples of the view B of thesecond camera are taken as the target domain sample Allcollected samples are manually marked In this manuscriptthe performance of the model is assessed by the accuracymeasurement defined by

Accu naccu

Num (7)

where naccu is called the number of the correct trajectoryclassification and Num is called the total number of the testdata


42 Analysis of Experimental Results )e first experimentaims to qualitatively compare the performance of the HMMtransfer method described in this manuscript with the onethat existed in the literature [9] In this experiment k is set tosome sample values such as (k 10 15 20 25 30 40 and 50)representing each type of the trajectory in the sample set ofthe target domain that is randomly selected and combinedwith the sample set of the source domain as the training dataIn addition to k number of the selected samples all otherdata in the sample set of the target domain are employed asthe test data Figures 10ndash12 are the comparisons of theaccuracies of the test data between the source and the targetdomains when the number k of each type of trajectorysample changes with the angle of the view θ 30deg θ 45degand θ 60deg respectively )e experimental results suggestthat the accuracy of the method in the experiment is

improved with the increment of the number of the targetdomain samples k As the number of the target domainsamples increases the learning algorithm could extract moreknowledge from the target domain When only θ 60deg theaccuracy of trajectory 2 does not improve or even decreasesindicating that overfitting occurs in this case It is worthnoting that the accuracy of this algorithm increases fasterthan other algorithms with the increment of samples Whenthe included angle varies from 30deg to 45deg and 60deg and k iskept constant the corresponding accuracy of most trajec-tories decreases indicating that the increment of the angle ofthe view leads to more obvious deformation of the trajectoryat different included angles (Figure 12) )e experimentalresults also suggest that when compared with the methodresearched in [9] this method could achieve a higher rec-ognition rate of the behavior trajectory of the cross-view

Table 5 Steps of the algorithm of the transition probability optimization

Steps of the algorithm of the transition probability optimization(1) Simulate the trajectory samples by model λ(1113954AT BT and πT)

(2) Calculate the similarity between simulation set and target domain label sample set sim(3) While simgtδSolve ΔA according to the interior point method update 1113954ATto 1113954AT + ΔASimulate trajectory samples via the model λ(1113954AT BT and πT)

Calculate the similarity between simulation set and target domain label sample set simEND While

Optimizationalgorithm

Least squaremethod

Maximum RecognitionP (O|λT)

Source domain view Target domain view

Linear regression

Simulation data

Similaritycalculation

Interior point method

AT

Source domainlable samples

Target domainlable sample set

Target trajectory modelλT = (AT BT πT)


Initial target modelparameters

λ = (AS + ΔA BT πT)

Source trajectorymodel

λS = (AS BS πS)

Target domainunlable sample set

Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25

Figure 9 )e HMM transfer method framework λS (AS BS and πS) represents the source domain of the HMM λT (AT BT πT)

represents the target domain of the HMM P(O|λT) is called the probability of the occurrence of the observation value sequence O in themodel λT


target utilizing only a small amount of the marked data fromthe target domain perspective which would greatly reducethe annotation work of the target domain perspective

In the second experiment according to the results ofthe previous experiment the number of training data ofthe target domain perspective is fixed to 50 To verify theeffectiveness of this method the proposed method iscompared with both Method 1 and Method 2 and theresults are recorded In Method 1 the marked trainingdata from view B are utilized to find out the parameters ofthe model )e marked data in the number of view B aresmall so the leave-one-out cross-validation technique isimplemented In this technique a group of 20 samples istaken from the target domain data set as the test set therest are left as the training data until all samples have been

tested A total of M times (the size of the data set) areconducted and calculated and finally the accuracy isaveraged In Method 2 only the marked training data inview A are utilized to conduct the BaumndashWelch algorithmto attain the HMM and the determined parameters of themodel are utilized to attain the accuracy of the test data setof view B

Tables 6ndash8 present the accuracy rates of the differentmethods at the different θ values )e purpose of thecomparison with Method 1 is to decide whether a trainedmodel of the source domain could be utilized directlyacross visual angles)e results imply that the effect is poorespecially from different views since the knowledgeextracted from the source domain cannot be directly ap-plied to the target domain especially when the two

Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)

Figure 10 )e comparison between the proposed method and the method in [9] on the change of the accuracy in testing data utilizing thenumber of the target domain markers (θ 30deg) (a) Trajectory 1 (b) Trajectory 2 (c) Trajectory 3 (d) Trajectory 4


domains differ much Compared with Method 1 themethod in this manuscript greatly improves the outcomesof the recognition )is indicates that although the HMMtrajectory modeling is very successful when implementedfrom a single perspective its performance would signifi-cantly decrease when both cross views and crossing viewhave a great impact on trajectory recognition Comparedwith Method 2 the recognition effect is similar indicatingthat when a small data set of the target domain are pro-vided the performance of the HMM transfer model isalmost the same as that of the training model with a largedata set of the target domain In conclusion the transferlearning method in this manuscript makes use of the priorknowledge that has been already extracted in the sourcedomain model and hence could effectively identify the

cross-view target trajectory Besides it does not require ahigh number of target domain samples Since there areenough samples in the source domain which contains alarge amount of characteristic information the transferlearning could utilize only a small target data set tocombine with these prior pieces of knowledge to attainbetter outcomes

In the third experiment according to the outcomes ofthe first experiment the training data of the target domainperspective are fixed to 50 and the performance of theproposed method is compared with the HMM transfermethod described in the literature [10 11]

Seen from Tables 9ndash11 that the HMM transfer methodin this manuscript is more effective than other HMMtransfer methods under the same experimental settings

Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)


Table 6 )e accuracies of Method 1 Method 2 and the proposed method (θ 30deg)

Methods Method 1 Method 2 )e proposed methodTrajectory 1 095 063 092Trajectory 2 085 061 090Trajectory 3 090 037 088Trajectory 4 100 041 091Average 093 048 090




In the transfer recognition of the cross-view HMM tra-jectory model the accuracy rate of the proposed methodreaches over 85 in most cases and the half could be over90

)e experiments present that the linear regressionmodel based on the least square method can be suc-cessfully applied to the transfer learning method of targetbehavior recognition )e characteristic representation ofboth the source domain and target domain differs due tothe variation of a visual point To overcome this issue weneed to find statistical patterns between the characteristicsof the source domain and the target domain )en thecurve needs to be fitted By doing so transferring theprobability distribution of the emission of the sourcedomain adaptively is transferred to the target domainHence it leads to transferring the correlation knowledgebetween different perspectives and behaviors from onedomain to another )e existence of a small number of thelabeled samples in the target domain provides a referencefor the optimization of the state transition probability ofthe source domain )e improved and optimized HMM

performs well on the data set with higher accuracy andbetter robustness

5 Conclusion

)is manuscript mainly deals with identifying the behaviorcategories of the trajectory data of the target behavior whenthe cross perspective is a concern In the case of havinginsufficient labeling data of the target domain having dif-ficulty in labeling data and dealing with a higher cost theproblem is transformed into the identification problem ofthe feature sequence of the trajectory utilizing the HMMtransfer learning )rough knowledge transfer of relevantdata from different perspectives the classification model isconstructed and then the behavior trajectory category of thedata to be classified in the target domain is identified In thismanuscript first according to the data that is labeled fromthe perspective of the source domain an HMM is con-structed to train the parameters of the triples second thefrequency of the coding sequence features utilizing the sametype of data that is labeled from the perspectives of the



Table 9 )e accuracies of the methods in the [10 11] and the proposed method (θ 30deg)

Methods )e method in [10] )e method in [11] )e proposed methodTrajectory 1 081 075 092Trajectory 2 079 086 090Trajectory 3 084 088 088Trajectory 4 091 078 091Average 084 082 090

Table 11 )e accuracies of the methods in [10 11] and the proposed method (θ 60deg)



Method s )e method in [10] )e method in [11] )e proposed methodTrajectory 1 090 068 090Trajectory 2 074 080 087Trajectory 3 082 088 087Trajectory 4 087 079 090Average 083 079 089


source domain and target domain is computed )en themapping curves of the two perspectives are fitted by the leastsquare Hence the observed probability matrix is adaptivelytransferred by mapping relationships Afterward the tran-sition probability based on a small labeled data of the targetdomain is transferred to the target domain through anoptimization algorithm )erefore the target domain clas-sification model is constructed )e experimental results onthe data set denote that the transfer learning method basedon the HMM could construct the classification model and ithas a better performance in the recognition of the cross-viewtarget trajectory when there exist a small number of labeleddata in the target domain perspective

Data Availability

All the data are included in the manuscript and further datacan be requested from the corresponding author uponreasonable request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (no 61673318 target trace analysis andabnormal behavior warning in structural space) the KeyIndustrial Chain Project of Shaanxi Province (no2020ZDLGY04-04) and the Science and Technology Plan-ning Project of Xirsquoan City (no GXYD141 intelligentidentification system of residue state for Subwayconstruction)

References

[1] P Qiming and Y Cheng ldquoTrajectory recognition of movingobjects based on the hidden markov modelrdquo Computer Ap-plication Research vol 25 no 7 pp 1988ndash1991 2008

[2] B Dapeng Y Shanshan Z Shi Y Minghui andW Yun ldquo)emethod of fleet call and search based on hidden markovmodelrdquo 2020

[3] A Hervieu P Bouthemy and J P L Cadre ldquoAn HMM-basedmethod for recognizing dynamic video contents from tra-jectoriesrdquo in Proceedings of the IEEE International Conferenceon IEEE ICIP 2007 San Antonio TX USA 2007

[4] L Qian and H C Lau ldquoA layered hidden markov model forpredicting human trajectories in a multi-floor buildingrdquo inProceedings of the IEEEWICACM International Conferenceon Web Intelligence and Intelligent Agent Technology (WI-IAT) ACM Singapore 2015

[5] G Lin B Yun and Z Weigong ldquoRecognition of abnormalinteractions based on coupled hidden Markov modelsrdquoJournal of Southeast University vol 43 pp 1217ndash1221 2003

[6] R Vasanthan G Ver Steeg A Galstyan and A TartakovskyldquoCoupled hidden Markov models for user activity in socialnetworksrdquo in Proceedings of the IEEE International Conferenceon Multimedia amp Expo Workshops IEEE San Jose CA USA2013

[7] P Kumar G Himaanshu P Roy and D P Dogra ldquoCoupledHMM-based multi-sensor data fusion for sign languagerecognitionrdquo Pattern Recognition Letters vol 86 2017

[8] L Qian and H C Lau A Layered Hidden Markov Model forPredicting Human Trajectories in a Multi-Floor Building IEEEComputer Society Washington DC USA 2015

[9] T L M Van Kasteren G Englebienne and B J A KroseldquoRecognizing activities in multiple contexts using transferlearningrdquo in Proceedings of the AAAI Fall Symposium AI inEldercare New Solutions to Old Problems Arlington VI USA2008

[10] V W Zheng Q Yang W Xiang and D Shen ldquoTransferringlocalization models over timerdquo in Proceedings of the 23rdAAAI Conference on Artificial Intelligence pp 1421ndash1426Chicago IL USA July 2008

[11] G Bingtao Z Yang and L Bin ldquoBioTrHMM biomedicalnamed-entity recognition algorithm based on transferlearningrdquo Computer Application Research vol 36 no 1pp 51ndash54 2019

[12] D K Kim and N S Kim ldquoMaximum a posteriori adaptationof HMM parameters based on speaker space projectionrdquoSpeech Communication vol 42 no 1 pp 59ndash73 2004

[13] N S Kim J S Sung and D H Hong ldquoFactored MLLRadaptationrdquo IEEE Signal Processing Letters vol 18 no 2pp 99ndash102 2011

[14] O Siohan C Chesta and C-H Chin-Hui Lee ldquoJoint max-imum a posteriori adaptation of transformation and HMMparametersrdquo IEEE Transactions on Speech and Audio Pro-cessing vol 9 no 4 pp 417ndash428 2001

[15] K Ait-Mohand T Paquet and N Ragot ldquoCombiningstructure and parameter adaptation of HMMs for printed textrecognitionrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 36 no 9 pp 1716ndash1732 2014

[16] X Fei Y Xie S Tang and J Hu ldquoIdentifying click-requestsfor the network-side through traffic behaviorrdquo Journal ofNetwork and Computer Applications vol 173 Article ID102872 2021

[17] F Liu D Janssens J Cui G Wts and M Cools ldquoCharac-terizing activity sequences using profile hidden markovmodelrdquo Expert Systems with Applications vol 42 no 13pp 5705ndash5722 2015


related to the learning of the cross-domain knowledge andcould realize the model migration when the data of thetarget domain is unlabeled and the data of the sourcedomain is called a multisource Moreover it has a hightheoretical value in many practical problems Transferlearning which relaxes two basic assumptions in tradi-tional machine learning is a new method in the field ofmachine learning Its main characteristics could besummarized as follows (1) there must be enough samplesto learn for a good classification model (2) Both thetraining samples were utilized for learning and the newtest samples meet the conditions of independence andidentical distribution properties Some scholars haveproposed various HMM transfer methods for some cross-domain applications For instance Van Kasteren et alpropose that a parameter transfer learning method utilizesthe HMM that constructs the sensor mapping relationshipaccording to the location information of the spatialstructure and then finds out the parameters of the HMMutilizing the EM algorithm [9] Zheng et al propose that ittakes the received real-time signal intensity of mobiledevices as the observed value to construct the HMMpositioning model and realizes the transfer of it at dif-ferent times in the same position [10] Bingtao et alsuggest that giving weight to the sample data of the sourcedomain by calculating the similarity between the sourcedomain and the target domain sample data then finds outthe HMM parameters in the weighted data set and im-proves the learning algorithm to realize the instance-based HMM transfer learning [11] Similar researchstudies conducted by Kim et al propose that an HMMtransfer method utilizing the maximum a posterior(MAP) and maximum likelihood linear regression(MLLR) is applied to speech and text recognition [12ndash15]Some empirical research studies related to HMM are Feiet al in [16 17]

As a contribution to this research area to solve the low-cost application problem of the HMM trying to determinethe trajectory behavior in different perspectives this man-uscript proposes an HMM-based transfer learning andrecognition method for the behavior of the target trajectorywhere the cases consist of the perspective samples of thesufficient source domain and the perspective samples of fewmarked target domain exist )is method achieves thepurpose of transfer learning and recognition by transferringthe trajectory behavior model in the source perspectivedomain and optimizing a small number of samples in thetarget domain which provides an effective way to resolve thementioned problem

2 The Proposed Model Trajectory Modelingand Simulation

21 Target Trajectory Model Based on the HMM HiddenMarkov model (HMM) is a probabilistic model describingthe process of time series which can be described by fivecomponents denoted by a quintupleλ (N M A B and π) Moreover its simplified form isrepresented by λ (A B and π)

(1) N indicates the number of hidden states in themodel All states in the model are interconnectedand any state can be reached from other states

(2) M represents the observation symbol of each hiddenstate in the model ie the number of observationstates

(3) A is called the probability distribution of state tran-sition A aij1113966 1113967 where aij p(Qt+1 j|Qt i)0le aij le 1 and 1113936

Ni1 aij 1 1le i jleM Qt is called

the hidden state at time t(4) B is called the probability distribution of the observable

state in the hidden state at moment j B bik1113864 1113865 wherebik p(Qt k|Qt i) and 1le ileN 0le kleM Qt iscalled the observable state at time t

(5) π is called the distribution of the initial state π πi1113864 1113865where πi p(Q0 i) 1le ileN

According to the basic definition of the HMM thismanuscript firstly conducts the HMM modeling for thetarget trajectory )e direction angle of the trajectory of thetarget in a unit of time is utilized as the observation char-acteristic )e sequence of the angle representing the tra-jectory information is called the observable state vector )ehidden state is called the transfer characteristic of the anglechange of the target trajectory )e angular direction of thetarget trajectory is computed by

φt tanminus1 yt minus ytminus1

xt minus xtminus11113888 1113889 (1)

where (xt yt) and (xtminus1 ytminus1) are called the target positionsat time t and tminus 1 respectively According to φt the observedvalue Qt is attained by discretizing the 24-direction freemancode depicted in Figure 1)e parameters of the trajectory ofthe HMM are obtained by training

)e trajectory presented in Figure 2 is utilized formodeling )e coordinate sequence of the target trajectory ispresented in Table 1)e angle characteristic is computed by(1) and its discretization is presented in Table 2 While thenumber of the hidden states called N is set to 4 that ofobservation called M is set to 24 )e probability vector ofthe initial state denoted by π is defined as uniform distri-bution )e transfer probability and the probability distri-butions of the observation are initialized randomly )etrajectory samples above are trained by the BaumndashWelchalgorithm to attain the parameters of the initial distributionπ transfer probability matrix A and observation probabilitymatrix B respectively that are presented in Table 3

22 Simulation of the Target Trajectory )ere are two im-portant assumptions in the HMM which are expressed asfollows (1) homogeneous Markov Chain hypothesis that isthe hidden state at any time only depends on its previoushidden state (2) Observation independence hypothesis thatis the observed state at any time only depends on the hiddenstate at the current time

As presented in Figure 3 the hidden Markov Chainbased on the above hypothesis is determined by the initial











P1 P2 P3 P4 P5 P6 P7 P8 P9 P10X 280 278 275 272 270 269 266 262 258 252Y 155 157 160 169 169 170 173 177 182 189

1

2

34

56789

10

11

12

13

14

15

1617 18 19 20

2122

23

24


(a) (b)






Markov chain(π A)

Random sequence(B)


sequence






π1 41 00000 00000 10000 00000A1 1 4 00024 09976 00000 00000A2 1 4 00000 00000 00536 09464A3 1 4 10000 00000 00000 00000A4 1 4 09044 00000 00956 00000B1 7 12 00000 00000 00000 09261 00000 00739B2 7 12 00000 00000 00000 07153 02831 00000B3 7 12 00000 00000 00000 07169 02831 00000B4 7 12 00835 01670 04174 00015 03306 00000

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(a)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(b)

Figure 4 Continued





Ot wOs + b (2)


700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(c)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(d)


(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)



(a) (b)


Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100



Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700




1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References




























P1 P2 P3 P4 P5 P6 P7 P8 P9 P10X 280 278 275 272 270 269 266 262 258 252Y 155 157 160 169 169 170 173 177 182 189

1

2

34

56789

10

11

12

13

14

15

1617 18 19 20

2122

23

24


(a) (b)






Markov chain(π A)

Random sequence(B)


sequence






π1 41 00000 00000 10000 00000A1 1 4 00024 09976 00000 00000A2 1 4 00000 00000 00536 09464A3 1 4 10000 00000 00000 00000A4 1 4 09044 00000 00956 00000B1 7 12 00000 00000 00000 09261 00000 00739B2 7 12 00000 00000 00000 07153 02831 00000B3 7 12 00000 00000 00000 07169 02831 00000B4 7 12 00835 01670 04174 00015 03306 00000

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(a)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(b)

Figure 4 Continued





Ot wOs + b (2)


700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(c)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(d)


(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)



(a) (b)


Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100



Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700




1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References






















Markov chain(π A)

Random sequence(B)


sequence






π1 41 00000 00000 10000 00000A1 1 4 00024 09976 00000 00000A2 1 4 00000 00000 00536 09464A3 1 4 10000 00000 00000 00000A4 1 4 09044 00000 00956 00000B1 7 12 00000 00000 00000 09261 00000 00739B2 7 12 00000 00000 00000 07153 02831 00000B3 7 12 00000 00000 00000 07169 02831 00000B4 7 12 00835 01670 04174 00015 03306 00000

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(a)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(b)

Figure 4 Continued





Ot wOs + b (2)


700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(c)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(d)


(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)



(a) (b)


Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100



Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700




1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References






















Ot wOs + b (2)


700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(c)

700

600

500

400

300

200

100

00 200 400 600 800 1000 1200

(d)


(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)



(a) (b)


Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100



Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700




1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References



















(a) (b)


Freq

uenc

y

View 1View 2

0

10

20

30

40

50

60

70

80

90

100



Freq

uenc

y

View 1View 2

0

100

200

300

400

500

600

700




1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References



















1113944 Ot minus Ot( 11138572

1113944 Ot minus wOt + b( 1113857( 11138572 (3)




minΔA



d OT tOT( 1113857

1113944 OT minus tOT( 11138572

1113874 1113875

1113970

(5)



sim OT OT( 1113857 1

1 + d OT OT( 1113857 (6)






Accu naccu

Num (7)










Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References


























Least squaremethod



Linear regression

Simulation data



AT








λS = (AS BS πS)


Feature selection

πS BS πT BT

545

435

325

215

105

0

545

435

325

215

105

00 5 10 15 20 25 0 5 10 15 20 25








Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References























Accu

OurKasteren [9]

θ = 30deg

04

05

06

07

08

09

1

15 20 25 30 40 5010k

(a)

Accu

OurKasteren [9]

θ = 30deg

04

045

05

055

06

065

07

075

08

085

09

15 20 25 30 40 5010k

(b)

Accu

θ = 30deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 30deg

045

05

055

06

065

07

075

08

085

09

095

OurKasteren [9]

15 20 25 30 40 5010k

(d)







Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References























Accu

θ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 45deg

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(b)

Accu

θ = 45deg

03

04

05

06

07

08

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 45deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)



Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References



















Accu

θ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(a)

Accu

θ = 60deg

OurKasteren [9]

15 20 25 30 40 5010k

05

055

06

065

07

075

08

085

09

(b)

Accu

θ = 60deg

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(c)

Accuθ = 60deg

04

045

05

055

06

065

07

075

08

085

09

OurKasteren [9]

15 20 25 30 40 5010k

(d)










5 Conclusion












Data Availability




Acknowledgments


References






















5 Conclusion












Data Availability




Acknowledgments


References




















Data Availability




Acknowledgments


References



















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TransferLearningandIdentificationMethodofCross-ViewTarget … · 2020. 12. 24. · 4.2.AnalysisofExperimentalResults. eﬁrstexperiment aimstoqualitativelycomparetheperformanceoftheHMM