Local temporal common spatial patterns modulated with phase locking value
Introduction
The manifold structure of electroencephalogram (EEG) time series is useful for designing EEG-based brain–computer interfaces (BCI), in which a critical issue is to decode different mental activities as accurate as possible [12]. For this purpose, discriminative features are critically desirable. In literature, plenty of modern machine learning strategies are employed to extract classification features as discriminative as possible [15], [32].
As a successful paradigm, the formulation of common spatial patterns (CSP) [6] is a classical and effective technique for extracting features by using spatial filters. Based on the neurophysiological effect of event-related desynchronization and synchronization (ERD/ERS) appeared with μ- and β-rhythms [20], CSP maximizes a spatially filtered variance of one class and meanwhile minimizes that of another class. Due to the effectiveness of CSP, it has been intensively explored in the field of BCI [8], [17]. A large number of CSP extensions have been studied, such as common spatio-spectral patterns (CSSP) [14], regularized CSP (RCSP) [16], sparse CSP (SCSP) [3], stationary CSP (sCSP) [23], and Kullback–Leibler-based discriminant CSP (KLCSP) [4], [22]. We have developed L1-norm-based CSP [28] for robust EEG classification and comprehensive CSP (cCSP) for semisupervised learning [29]. In recent years, CSP still receives increasing attention by researchers. Some new methods continue to occur including probabilistic CSP [31], regularized sensor covariance matrices [21], separable common spatio-spectral patterns [1], as well as connection with deep learning [24].
Although the CSP-based spatial filtering approaches achieve satisfying classification performance in some situations, they are global methods in terms of processing EEG samples. That is, the manifold structure of EEG time series is neglected. To remedy this shortcoming, we have developed local temporal CSP (LTCSP) [30] to address the temporally local manifold of EEG time series. By designing temporally local variances based on a basic technique of machine learning, LTCSP characterizes the temporally local structure of EEG signal. If using correlation to design the weights in the temporally local variances, a variant of LTCSP, called local temporal correlation CSP (LTCCSP), is developed [33]. It is, however, beneficial to discover the intrinsic manifold of EEG time series from the perspective of neurophysiological information. In neurophysiological community, it is generally agreed that phase synchronization reflects signal communication [27], [25] and thus latently underlies different time points of EEG signal. The EEG samples with phase synchronization are in fact intrinsically “close”. Learning such kind of manifold may yield discriminative features. Specifically, if incorporating the phase synchronization into the framework of the temporally local manifold learning, we may obtain an enhanced spatial filtering approach. It combines the spatial amplitude and the temporal phase information.
In this paper, we consider performing temporally local manifold learning by explicitly incorporating the information of phase synchronization into the framework of LTCSP. The classical index of phase locking value (PLV) [13] is employed to quantify the phase synchronization. Specifically, we reformulate the temporally local variances by designing a weight function based on PLV rather than the amplitude of EEG signal. The larger the PLV quantity between two samples is, the heavier weight is endowed. We term the proposed method as PLV-modulated LTCSP (p-LTCSP). Finally, the extracted features of p-LTCSP are fed into the classifier of Fisher linear discriminant analysis (LDA) [9]. It is worthwhile to highlight three main properties of the proposed p-LTCSP approach as follows. (a) The PLV quantity, which is a classical index of quantifying the phase synchronization, is introduced into the framework of LTCSP to discover the intrinsically local manifold. (b) p-LTCSP is an enhanced spatial filtering approach which meanwhile utilizes the temporal phase information. (c) Like LTCSP, p-LTCSP is computationally efficient by simultaneously diagonalizing two temporally local covariance matrices.
The rest of this paper is organized as follows. The methods of CSP and LTCSP are briefly reviewed in Section 2. In Section 3, we introduce the p-LTCSP method, including instantaneous phase with PLV, LTCSP with PLV as weight, feature extraction and classification. The experimental results are reported in Section 4. Finally, Section 5 concludes this paper.
Section snippets
Brief review of CSP and LTCSP
Both CSP and LTCSP aim to produce spatial filters based on multi-channel EEG time series for a two-class paradigm. Assume that are EEG trials of one class (corresponding to one mental activity) while the other class (corresponding to the other mental activity), where c and n denote the number of EEG channels and the number of sampling time points respectively, and Tx and Ty the numbers of trials recorded under the two
Motivation
While LTCSP is an effective method of capturing temporally local manifold of EEG time series, the determination of the intrinsic manifold (embodied by the weight function) is still an open problem. By using the basic technique of machine learning, previously designed functions are based on the relation of amplitudes of EEG signal. The neurophysiological information, however, is not taken into account in the design of manifold learning. From the neurophysiological perspective, it is generally
Experiments
The experiments are performed on three publicly available EEG data sets of BCI competitions: data set IIIa of BCI competition III, data set IVa of BCI competition III, and data set IIa of BCI competition IV. The classification performance of the proposed p-LTCSP is compared with the conventional LTCSP and LTCCSP methods. The experiments are further conducted when artificial noise is introduced into the data sets.
Conclusion
In this paper, a framework that incorporates PLV into LTCSP is proposed to perform single trial EEG classification in the task of motor imagery. The PLV is used to re-formulate the temporally local covariance matrices so as to discover the intrinsic manifold of EEG time series. The phase synchronization is related to signal communication and cognitive activity, and thus underlies EEG time series latently. Consequently, the proposed p-LTCSP method extracts spatial filters based on amplitude
Authors’ contribution
HW, ZL and HF: designed the study; ZY, TM and NF: analyzed the data and performed experiments; ZY, TM and HW: drafted the manuscript and revised the manuscript. All authors approved the final version of the manuscript.
Acknowledgment
The authors would like to thank the anonymous referees for the constructive recommendations, which greatly improve the paper. This work was supported in part by the National Natural Science Foundation of China under grant 61773114, and the Key Research and Development Plan (Industry Foresight and Common Key Technology) of Jiangsu Province under grant BE2017007-3.
Conflict of interest: None declared.
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