title: Tensor decomposition of EEG signals: a brief review.
abstract: Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higher-order partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously.
authors.affiliation: Department of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China; Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland. Electronic address: cong@dlut.edu.cn.
authors.forename: Fengyu
authors.initials: F
authors.lastname: Cong
authors.affiliation: School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.
authors.forename: Qiu-Hua
authors.initials: QH
authors.lastname: Lin
authors.affiliation: School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.
authors.forename: Li-Dan
authors.initials: LD
authors.lastname: Kuang
authors.affiliation: School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.
authors.forename: Xiao-Feng
authors.initials: XF
authors.lastname: Gong
authors.affiliation: Department of Psychology, University of Jyväskylä, Jyväskylä, Finland.
authors.forename: Piia
authors.initials: P
authors.lastname: Astikainen
authors.affiliation: Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland.
authors.forename: Tapani
authors.initials: T
authors.lastname: Ristaniemi
mesh_terms: D001921:Brain / Q000502:physiology; D004569:Electroencephalography / Q000379:methods*; D005071:Evoked Potentials; D005163:Factor Analysis, Statistical; D016018:Least-Squares Analysis; D012815:Signal Processing, Computer-Assisted
keywords: Brain; Canonical polyadic; EEG; Event-related potentials; Signal; Tensor decomposition; Tucker