Higher Order Statistics and Phase Synchronization as Features in a Motor Imagery Paradigm

The paper proposes an approach based on higher order statistics and phase synchronization for detection and classification of relevant features in electroencephalographic (EEG) signals recorded during the subjects are performing motor tasks. The method was tested on two different datasets and the performance was evaluated using k nearest neighbor classifier. The results (classification rates higher than 90%) have shown that the method can be used for discriminating right and left motor imagery tasks as an offline analysis for EEG in a brain computer interface system. Keywords—Brain computer interface; motor imagery; higher order statistics; phase synchronization; EEG

Methods like autoregressive model [9], independent component analysis [10], wavelet transform [11] have been applied in order to extract relevant features contained in the EEG signal while a motor imagery task was performed.
The aim of the paper is to propose a combination of features which includes higher-order statistics (HOS) based on bispectrum and bicoherence and phase synchronization based on phase locking value and phase lag index. The features can be used for discriminating motor tasks in a motor imagery paradigm.
In Section II the handled datasets are described and Section III presents the methods, features extraction and classification. Section IV belongs to results and Section V to conclusions.

II. DATASETS DESCRIPTION
Dataset I contains EEG signals acquired in our laboratory. The brain activity was recorded using a gMobilab+ module [12] and BCI 2000 platform [13]. Dataset II was downloaded from the internet [14]. Table I presents the information regarding the manipulated datasets. III. METHODS Higher order spectra are expressed in terminologies of higher order statistics such as moments and cumulants of a random process, in this case EEG signals [15][16].
Bispectrum is commonly applied in the biomedical area mainly for EEG signal processing. Bispectrum is d in the bifrequency domain [15]: where ( ) is the Fourier transform of a windowed portion of a single realization of the EEG signal ( ), is an integer index, is the sampling period and [. ] represents the expectation operation.
Bicoherence is given by the following relationship [15][16] where ( ) is the power spectrum of ( ).
When the oscillatory phases from two brain regions are correlated the phase synchronization appears. The phase synchronization from the motor imagery period is different from the phase synchronization in the relaxation period so it can be exploited by BCI applications [17].
Large scale synchronization appears between brain signals acquired from electrodes located in the primary motor area and from electrodes located in the additional motor area.
Phase locking value (PLV) [17] and phase lag index (PLI) [18] are calculated in order to detect changes in the large scale synchronization and in order to measure the synchronization between two signals ( ) and ( ).
PLV represents the lastingness of the phase difference between instantaneous phases ( ) and ( ): The phase lag index is defined by: is the signum function and <. > denotes the time average.

A. Data Processing for Higher Order Statistics
Two sets of data were formed: one related to right hand movement imagery and the other corresponding to left hand movement imagery.
First, the EEG signals aquired from channels C3, C4, CP3, CP4, P3, P4 when the subject imagined the right hand movement were segmented in 30 (Dataset I) and 45 (Dataset II). The bispectrum and bicoherence were estimated using functions from HOSA toolbox [19]. Two different frequency ranges were extracted for analysis in the bi-frequency plane (f1 -f2): Mu -Mu, Beta -Beta. The module of the bispectrum was calculated for these frequency ranges. In the next step only the elements above the main diagonal (those below the main diagonal being equal to those above) were extracted for the two frequency ranges.
A direct method is applied to estimate the bicoherence.
Four quantity measures for each frequency range were settled: the sum of the bispectrum modules, the sum of the squares bispectrum modules, the sum of the bicoherence modules, the sum of the squares bicoherence modules.
The steps described above were followed for the EEG signals corresponding to left hand motor imagery.

B. Data Processing for Phase Synchronization
Four sets of data were created: the right hand movement imagery, the rest after right hand movement imagery, the left hand movement imagery and rest after left hand movement imagery. In order to compute PLV and PLI, the instanteneous phase of the EEG signals must be determined. The instanteneous phase of the EEG signals is computed using Hilbert transform. The Hilbert transforms were calculated for the EEG channels mentioned.
One electrode from the auxiliary motor imagery area, Cz, three electrodes from the right hemisphere, C4, CP4, P4 and three electrodes from the left hemisphere, C3, CP3, P3 were utilized in order to establish the combinations. The completed pairs of electrodes were: Cz-C4, Cz-CP4, Cz-P4, Cz-C3, Cz-CP3, Cz-P3. The differences between PLVs of the rest period and motor imagery period were formed for the above pairs of electrodes.
The steps mentioned above were repeated for PLI.

C. Feature Vectors
Nine feature vectors were created by bringing together two, three or four of the already mentioned measures. So, the first feature vector is formed by bicoherence and PLV, the second by bicoherence and PLI, the third by bicoherence, PLV and PLI, the fourth by bispectrum and PLV, the fifth by bispectrum and PLI, the sixth by bispectrum, PLV and PLI, the seventh by bicoherence, bispectrum and PLV, the eighth by bicoherence, bispectrum and PLI and the ninth by bicoherence, bispectrum, PLV and PLI. These nine feature vectors were named according to their way of grouping: Bicoherence_PLV was attributed for the feature vector combining bicoherence and PLV, Bicoherence_PLI for the feature vector merging bicoherence and PLI, and so on.
The discrimination between right and left motor imagery was evaluated with k nearest neighbor (kNN) [20]. The performance of classifier was assessed through classification rate, sensitivity and specificity. The classification rate, the specificity and the sensitivity are characterized using the = + (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 12, No. 8, 2021 130 | P a g e www.ijacsa.thesai.org IV. RESULTS In Fig. 1 is displayed the bispectrum of an EEG signal corresponding to right hand motor imagery for channel C3 (Dataset I) and Fig. 2 illustrates the bispectrum of an EEG signal corresponding to left hand motor imagery for channel C4 (Dataset I). The bicoherence of an EEG signal corresponding to right hand motor imagery for channel C3, respectively the bicoherence of an EEG signal corresponding to left hand motor imagery for channel C4 are shown in Fig. 3 and Fig. 4.  From the above figures we can see that the bispectrum and the bicoherence yielded to different graphs for EEG signal corresponding to right versus left hand motor imagery and this suggests that can be used as feature vectors for classification. Fig. 5 shows the box plots for the classification rate, the sensitivity and the specificity using as feature vectors Bicoherence_PLV, Bicoherence_PLI and Bicoherence_PLV_PLI for Dataset I. The highest value (90%) of the median for classification rates was obtained for Bicoherence_PLV_PLI and all the subjects attained classification rates in the range 84% to 94%.   The box plots for the classification rate, the sensitivity and the specificity using as feature vectors Bispectrum_PLV, Bispectrum_PLI and Bispectrum_PLV_PLI -Dataset I are displayed in Fig. 6. The medians for the classification rates, the sensitivities and the specificities obtained were above 88% for Bispectrum_PLV_PLI. The outliner marked in blue color represents the highest classification rate attained (the value isn't relevant since belongs to a single subject). In Fig. 7 are presented the box plots for the classification rate, the sensitivity and the specificity using as feature vectors Bicoherence_Bispectrum_PLV, Bicoherence_Bispectrum_PLI and Bicoherence_Bispectrum_PLV_PLI -Dataset I. The highest classification rates, sensitivities and specificities were realized for Bicoherence_Bispectrum_PLV_PLI.  Fig. 8 shows the box plots obtained for the classification rate, the sensitivity and the specificity using as feature vector Bicoherence_PLV, Bicoherence_PLI and Bicoherence_PLV_PLI -Dataset II. The highest classification rates were for Bicoherence_PLV_PLI. The outliners marked with "*" for all the figures are for Subject 9.  Fig. 9 displays the box plots achieved for the classification rate, the sensitivity and the specificity using feature vector Bispectrum_PLV, Bispectrum_PLI and Bispectrum_PLV_PLI -Dataset II. Overall, the best classification rates (85%), sensitivities and specificities were obtained for Bispectrum_PLV_PLI . The box plots for the classification rate, the sensitivity and the specificity using as feature vector Bicoherence_Bispectrum_PLV, Bicoherence_Bispectrum_PLI and Bicoherence_Bispectrum_PLV_PLI -Dataset II are presented in Fig. 10. Comparing to the other feature vectors, the smallest classification rates, sensitivities and specificities were obtained for the feature vectors from Fig. 10. In Table II are summarized the maximum and the median of the classification rates for Dataset I and Dataset II attained with the mentioned feature vectors. The best classification rates were attained for feature vector Bicoherence_PLV_PLI for both datasets.
In [22] where a framework for achieving subject transfer strategy is proposed, the classification rates obtained for subject 9 were in the range 57.93% to 70.93% with linear discriminant analysis. The results are consistent with the results obtained with our feature vectors.
In [23] where was investigated a method based on multiple frequency spatial synthesized features with support vector machine classifier, the classification accuracies were smaller than the results reported in this paper. In [24], [25] were manipulated only PLV and PLI without being in combinations with other methods, but more channels were taken into account. The results achieved in these two cited works are approximately the same with the results stated in this paper with feature vector Bicoherence_PLV_PLI. The maximum classification rates of 86% are attained using PLI and SVM classifier.
V. CONCLUSION An offline analysis was performed on two datasets that contained 57 subjects and 9 subjects. Using combinations of bispectrum, bicoherence, phase locking value and phase lag index, nine features vectors were formed.
By means of Bicoherence_PLV_PLI as feature vector and kNN as classifier, the highest classification rates, sensitivities and specificities achieved for Dataset I were 93.90%, 94.35% and 94.29% respectively and for Dataset II were 91.86%, 94.56% and 90.67%, respectively.
The best classification rate attained with Bicoherence_PLV_PLI for both datasets highlights that, regardless of the database and of the conditions in which the electroencephalographic signals were recorded, the grouping of the three measures that compose this feature vector discriminates the best the two classes. The explanation might be linked to the fact that there are taken into account both the information of nonlinear interaction described by bicoherence and of the large scale synchronization described by PLV and PLI, and together they discriminate better than alone the two tasks.
The subjects from Dataset II were trained and the subjects from Dataset I were untrained. Even if the subjects from Dataset II were trained, the results obtained were worse than those for Dataset I. This fact suggests that the method used for creating feature vector Bicoherence_PLV_PLI is adequate to be used for discrimination of motor imagery tasks in a BCI, no matter the degree of subjects' training.
The future work implies testing the method on other available datasets that provide EEG signals recorded from the subjects while performing motor imagery tasks.