We propose an approach based on Hidden Markov models (HMMs) combined with principal component analysis (PCA) for classification of four-class single trial motor imagery EEG data for brain computer interfacing (BCI) purposes. We extract autoregressive (AR) parameters from EEG data and use PCA to decrease the number of features for better training of HMMs. We present experimental results demonstrating the improvements provided by our approach over an existing HMM-based EEG single trial classification approach as well as over state-of-the-art classification methods

Argunsah, Ali Ozgur

Argunşah, Ali Özgür

Cetin, Mujdat

Çetin, Müjdat

English

Sabanci University Research Database

AR-PCA-HMM Approach for Sensorimotor TaskClassification in EEG-based Brain-ComputerInterfacesAli O¨zgu¨r Arguns¸ah∗††Champalimaud Neuroscience Programmeat Instituto Gulbenkian de CieˆnciaOeiras, Portugalargunsah@igc.gulbenkian.ptMu¨jdat C¸etin∗∗Faculty of Engineering and Natural SciencesSabancı UniversityI˙stanbul, Turkeymcetin@sabanciuniv.eduAbstract—We propose an approach based on Hidden Markovmodels (HMMs) combined with principal component analysis(PCA) for classification of four-class single trial motor imageryEEG data for brain computer interfacing (BCI) purposes. Weextract autoregressive (AR) parameters from EEG data and usePCA to decrease the number of features for better trainingof HMMs. We present experimental results demonstrating theimprovements provided by our approach over an existing HMM-based EEG single trial classification approach as well as overstate-of-the-art classification methods.Keywords-BCI, EEG, HMMI. INTRODUCTIONElectroencephalography (EEG) based Brain-Computer In-terface (BCI) systems are a new development in the field ofapplied neurophysiology. These systems are being developedin order to enable people who cannot carry out normal motorfunctions, such as Amyotrophic Lateral Sclerosis (ALS) andTetraplegic patients, to control computer based devices.EEG is a time series signal. EEG-based BCI research isaimed at the development of signal processing and patternrecognition techniques to find specific patterns, for performingparticular actions, using features extracted from this time seriessignal. During the imagining of motor actions, the frequencystructure of the EEG signal changes through time [1]–[3].There are four different motor imagery tasks in the datawe have used (see section III-A). A different region in thebrain is responsible for each of these tasks. Although, thereis a correspondence between recording electrodes and brainregions, it is not one-to-one due to the volume conductioneffect of the brain tissues that make the electrical signal spreadall over the brain [4].When a subject does not process a sensory input or producea motor output, primary sensory or motor cortical areas displaya 8-12 Hz activity known as the µ rhythm [1]. The µ rhythmThis work was supported by the Scientific and Technological ResearchCouncil of Turkey under Grant 107E135, by a Turkish Academy of Sciences(TUBA) Distinguished Young Scientist Award and by a TUBA GraduateFellowship.decreases with movement, preparation of movement or imagi-nation of that movement [3], particularly in contra-lateral areasof the brain to the limb movement. This decrease is calledevent-related desynchronization (ERD). Similarly increasedrhythm is called event related synchronization (ERS) andoften appears after movement [3]. Various machine learningalgorithms have been used by BCI community such as linearclassifiers, neural networks, nonlinear Bayesian classifiers,nearest neighbor classifiers and the combinations of any ofthe above [5]–[7] to characterize the ERD and ERS patternsrecorded during different movement experiments. In this study,using data from different electrodes corresponding to motorimagery related brain regions for different tasks, we havemodeled the evolution of the frequency structure of the signalover time using HMMs.Hidden Markov Models (HMM) are dynamic classifiersused in a variety of fields, most widely in the field of speechrecognition [8]. An HMM is a kind of probabilistic automatonthat can provide the probability of observing a given sequenceof feature vectors. An HMM involves probabilities for tran-sition between the states, as well as conditional probabilitydensities of the observed feature vectors, given the underlyingstates. HMMs have been applied to the classification of 2-class temporal sequences of BCI features [9], [10] and evento the classification of raw EEG [11]. Although they are notvery widespread within the BCI community, they seem aspromising classifiers for BCI systems.In this paper, an HMM-based classifier based on autoregres-sive (AR) features is used within the context of BCI for thefirst time. AR features are good frequency estimators howevertheir rather high dimensions are problematic in the learningof the HMM parameters during training. To overcome thisproblem, we have proposed an approach based on principalcomponent analysis (PCA) to reduce the dimensions of ARfeatures, making them more suitable for HMM classifiers.This is the major technical contribution of this paper. Finally,this study applies HMM-based classification on a 4-class BCIproblem for the first time. We evaluate our approach basedon the BCI Competition IV-2a dataset, and demonstrate the2010 International Conference on Pattern Recognition1051-4651/10 $26.00 © 2010 IEEEDOI 10.1109/ICPR.2010.36113improvements it provides over existing techniques (see TableI).II. AR-PCA-HMM FOR CLASSIFICATIONA. Autoregressive FeaturesAR parameter estimation is one of the most commonlyused techniques to extract frequency related EEG features. Thepth order autoregressive (AR) model describes an EEG signalyk(t) at channel (electrode) k as:yk(t) = a1,ky(t−1) +a2,ky(t−2) + ...+ap,ky(t−p) +E(t)Here, ai,k denotes the ith order AR parameter modeling theEEG signal at channel k and E(t) is white noise with zeromean and finite variance. There is a direct correspondencebetween the AR parameters and the autocorrelation functionof the process, and this correspondence can be inverted todetermine the parameters from the autocorrelation functionusing the Yule-Walker equations. We have estimated ARparameters for each EEG channel that we have used for thisstudy using least-squares (LS) estimation. We have calculatedparameters for each single trial in overlapping windows. FourEEG channels were used namely C3, C4, Cz, Pz . These chan-nels correspond to the electrodes which are likely to provideinformative measurements about motor tasks. We have thefeature matrix F for each trial after the estimation:F =a1,C3(1), · · · , a1,C3(M).........ap,C3(1), · · · , ap,C3(M)a1,C4(1), · · · , a1,C4(M).........ap,C4(1), · · · , ap,C4(M)a1,Cz(1), · · · , a1,Cz(M).........ap,Cz(1), · · · , ap,Cz(M)a1,Pz(1), · · · , a1,Pz(M).........ap,Pz(1), · · · , ap,Pz(M)4p×MHere ai,k(m) is the AR parameter at the mth window and Mis the number of overlapping windows. From now on, eachcolumn of F will be represented as f cm if data are labeled andas fm if the data are not labeled, where m ∈ [1, . . . ,M ] andc ∈ [1, . . . , 4], with c denoting the class label.B. Principal Component AnalysisPCA is an orthogonal linear transformation that maps thedata into a new space, so called eigenspace, such that theelements of the transformed data are uncorrelated with eachother.Let fm be the r = 4p dimensional feature vector with zeromean and covariance matrix Σ. Eigenvalues and eigenvectorscan be calculated using eigendecomposition:Λm = WmΣmWTmwhere WTm is the eigenvector matrix of the covariance matrixΣm, and Λm is the corresponding diagonal matrix of eigenval-ues. These eigenvectors in this case are known as the principalcomponents. Consequently, projection to the eigenspace isachieved byzm = WmfmOne can reduce the dimension of the feature vector byordering eigenvalues and selecting the corresponding first scolumns of Wm where s < r.We compute one eigenvector matrix for each overlappingwindow separately. To do that, first we estimate features foreach trial using four electrodes as explained in section II-A.Then, we create the following matrix Gnm for each overlappingwindow by concatenating the data from same window ofdifferent classes:Gnm =[f1m, . . . , f4m]4.p×4where n ∈ [1, ..., N ] denotes the trial number and N corre-sponds to the total number of trials. For the sake of notationalsimplicity we ignore the dependence of f cm on the trial index n.Then, corresponding features from the corresponding windowsof each trial are concatenated:Hm =[G1m, · · · , GNm]4.p×4.NFor each overlapping window m, we estimate the covariancematrix of fm as Σˆm = HTmHm. Then Wm is found as thematrix of eigenvectors of Σˆm.First s rows (s < 4p) of each overlapping window specificWm matrix is used and represented as W sm to calculate eachreduced dimensional feature vector, where s is the number ofprincipal components that we want to reduce the dimensionto.jcm = WsmfcmFinally, by concatenating the reduced dimensional featurevectors we get the following reduced dimensional featurematrix Jctrain for each class:Jctrain = [jc1, jc2, . . . , jcM ]s×MWe apply the learned matrix W sm for dimensionality reductionof unlabeled test data. For each trial the number of featureswere reduced from 4p×M to s×M . The values of p and sused in the test data for each subject are shown in Table I.C. Hidden Markov Model LearningWe learn a different HMM for each of the four classes inour problem. We model the conditional probability densities ofthe reduced dimensional feature vectors given the underlyingstates with Gaussian mixtures. For each of these models, weconsider two sets of parameters to be learned. The first one,which we denote model-order parameters includes the numberof states (NoS) of the HMM, the number of Gaussian mixtures(NoGM), the AR model order p, and reduced dimension s(see Table I). We denote the second set of parameters asmodel parameters λc = {A,B,Π}. Here A is state transition114probabilities, B is the means and variances of the observationprobability distributions and Π is initial state distributions(see [8]). We split the data into three namely F ctrain (40%),F cvalidation (30%), Ftest (30%). For a fixed set of model-order parameters, we learn the model parameters based ontraining data F ctrain using the expectation-maximization (EM)algorithm so that the likelihood of the observed trainingsequences is locally maximized. We learn the model-orderparameters by maximizing the classification performance onvalidation data F cvalidation. We then test our classificationapproach on test data Ftest based on these learned parameters.III. EXPERIMENTAL RESULTSA. Experimental Setup and DataBCI Competition IV-2a dataset consists of EEG data from9 subjects. The cue-based BCI paradigm consisted of fourdifferent motor imagery tasks, namely the imagination ofmovement of the left hand (class 1), right hand (class 2), bothfeet (class 3), and tongue (class 4). Two sessions on differentdays were recorded for each subject. Each session is consistof 6 runs separated by short breaks. One run consists of 48trials (12 for each of the four possible classes), yielding a totalof 288 trials per session.The subjects were sitting in a comfortable armchair in frontof a computer screen. At the beginning of a trial (t = 0 s), afixation cross appeared on the black screen. In addition, a shortacoustic warning tone was presented. After two seconds (t =2 s), a cue in the form of an arrow pointing either to the left,right, down or up (corresponding to one of the four classesleft hand, right hand, foot or tongue) appeared and stayed onthe screen for 1.25s. The subjects were asked to carry out themotor imagery task until the fixation cross disappeared fromthe screen at t = 6s. A short break followed where the screenwas black again. The paradigm is illustrated in Figure 1b.(a) (b)Fig. 1: Electrode Configuration and Timing SchemeTwenty-two Ag/AgCl electrodes (with inter-electrode dis-tances of 3.5 cm) were used to record the EEG accordingto the international 10-20 system. All signals were recordedmonopolarly with the left mastoid serving as reference andthe right mastoid as ground (see Figure 1a). The signals weresampled at 250 Hz and bandpass filtered between 0.5 Hzand 100 Hz. An additional 50 Hz notch filter was enabledto suppress line noise. We have used the first sessions of first8 of the subjects. These same 8 subjects were also used in[12] and [13].B. ResultsFig. 2: Performance of the proposed AR-PCA-HMM approachas compared to other HMM-based techniques.TABLE I: Model-order parameters that gave best probabilityof correct classification results in validation dataset and usedin the test dataset.Method Parameters S1 S2 S3 S4 S5 S6 S7 S8AR-PCA-HMMp 14 15 14 14 15 14 15 15s 10 8 8 10 10 7 9 8NoGM 3 3 3 3 3 2 3 3NoS 5 5 5 3 5 5 5 5AR-HMMp 9 5 5 8 6 15 13 6NoGM 2 1 1 1 2 1 1 3NoS 4 2 3 4 1 2 3 3Hjorth-HMM NoGM 3 1 3 2 1 1 1 3NoS 5 3 1 5 3 1 4 1AR-Mahal p 10 8 5 7 9 5 6 9TABLE II: AR-PCI-HMM vs. State-of-the-art Techniques.κ = (C × PCC − 1)/(1 − C). κ approaches to zeroas the PCC approaches to 1/C where C is the number ofclasses.Feature / Classifier κmean S1 S2 S3 S4 S5 S6 S7 S8AR-PCA / HMM .65 .93 .91 .34 .36 .95 .01 .89 .81FBCSP / Naive Bayes .57 .68 .42 .75 .48 .40 .27 .77 .75CSP / LDA-Bayes .51 .69 .34 .71 .44 .16 .21 .66 .73CSP / SVM-Voting .30 .38 .18 .48 .33 .07 .14 .29 .49CSP / LDA-SVM .29 .46 .25 .65 .31 .12 .07 .00 .46CSP / SVM .28 .41 .17 .39 .25 .06 .16 .34 .45We show the probability of correct classification (PCC) ofour AR-PCA-HMM approach as compared to other HMM-based classifiers including the Hjoth-HMM approach of [14]in Figure 2. For 7 of 8 subjects, our approach achieves thehighest PCC. In Table II, we present a comparison of AR-PCA-HMM with the top techniques in BCI Competition IVon this dataset1, in terms of the κ coefficient. We observe thatAR-PCA-HMM achieves the best performance.1In our experiments, we have used the first part of the competition data,provided for use in algorithm development.115IV. CONCLUSIONSIn this paper, we have estimated autoregressive (AR) fea-tures from EEG data and used principal component analysis(PCA) to decrease the number of features for better trainingof HMMs to solve the four-class sensory motor EEG-basedBCI classification problem. The main idea of the paper wassupporting the use of AR features with HMM classifiers forthe EEG-based BCI problem.Results suggest that AR features are better features forHMM based EEG-BCI classifiers and dimension reduction iscrucial for EEG classification. 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AR-PCA-HMM approach for sensorimotor task classification in EEG-based brain-computer interfaces

Ali Ozgur Argunsah

Mujdat Cetin

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AR-PCA-HMM Approach for Sensorimotor Task Classification in EEG-based Brain-Computer Interfaces

http://research.sabanciuniv.edu/15658/1/argunsah_ICPR10.pdf

AR-PCA-HMM approach for sensorimotor task classification in EEG-based brain-computer interfaces

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