Local temporal common spatial patterns modulated with phase locking value

https://doi.org/10.1016/j.bspc.2020.101882Get rights and content

Highlights

  • Phase locking value is introduced to quantify phase relationship between EEG samples.

  • The above quantity is adopted as weight to define temporally local covariance matrix.

  • PLV-modulated LTCSP boils down to an eigenvalue decomposition problem.

Abstract

In the field of electroencephalogram (EEG)-based brain–computer interfaces (BCI), the method of common spatial patterns (CSP) is formulated as a problem of eigen-decomposition of covariance matrices. By using temporally local samples to construct the covariance matrices, the approach of local temporal common spatial patterns (LTCSP) are developed, which performs manifold modeling. It is useful to consider the intrinsic structure of samples in defining the temporally local covariance matrices. From the perspective of neurophysiological knowledge, phase synchronization indicates information communication. In this paper, we apply phase locking value (PLV) to quantify the phase relationship between samples, which are then adopted as weights to define the temporally local covariance matrices. As a result, we obtain the PLV-modulated LTCSP. More discriminative features are discovered with the approach proposed. Experiments of EEG classification on three EEG data sets (i.e., the data sets IIIa and IVa of BCI competition III and the data set IIa of BCI competition IV) demonstrate the effectiveness of the proposed technique. The average classification accuracies of the proposed method on the three data sets are 90.56%, 83.25%, and 83.26%. In the case of noise introduced, the average classification accuracy of the proposed method exceeds the conventional CSP and LTCSP by nearly 10% and 6%, respectively. The hypothesis test indicates the superiority of the proposed method in terms of statistical significance.

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 Xi={xki|k=1,,n}c×n(i=1,,Tx) are EEG trials of one class (corresponding to one mental activity) while Yj={ykj|k=1,,n}c×n(j=1,,Ty) 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.

References (33)

  • B. Blankertz et al.

    Optimizing spatial filters for robust EEG single-trial analysis

    IEEE Signal Process. Mag.

    (2008)
  • J. Demšar

    Statistical comparisons of classifiers over multiple data sets

    J. Mach. Learn. Res.

    (2006)
  • G. Dornhege et al.

    General signal processing and machine learning tools for BCI

    Toward Brain–Computer Interfacing

    (2007)
  • R.O. Duda et al.

    Pattern Classification

    (2001)
  • R. Eisinga et al.

    Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers

    BMC Bioinformatics

    (2017)
  • H.-J. Hwang et al.

    EEG-based brain–computer interfaces: a thorough literature survey

    Int. J. Hum.-Comput. Interface

    (2013)
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