TY - JOUR
T1 - Common Spatial Pattern Reformulated for Regularizations in Brain-Computer Interfaces
AU - Wang, Boyu
AU - Wong, Chi Man
AU - Kang, Zhao
AU - Liu, Feng
AU - Shui, Changjian
AU - Wan, Feng
AU - Chen, C. L.Philip
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2021/10/1
Y1 - 2021/10/1
N2 - Common spatial pattern (CSP) is one of the most successful feature extraction algorithms for brain-computer interfaces (BCIs). It aims to find spatial filters that maximize the projected variance ratio between the covariance matrices of the multichannel electroencephalography (EEG) signals corresponding to two mental tasks, which can be formulated as a generalized eigenvalue problem (GEP). However, it is challenging in principle to impose additional regularization onto the CSP to obtain structural solutions (e.g., sparse CSP) due to the intrinsic nonconvexity and invariance property of GEPs. This article reformulates the CSP as a constrained minimization problem and establishes the equivalence of the reformulated and the original CSPs. An efficient algorithm is proposed to solve this optimization problem by alternately performing singular value decomposition (SVD) and least squares. Under this new formulation, various regularization techniques for linear regression can then be easily implemented to regularize the CSPs for different learning paradigms, such as the sparse CSP, the transfer CSP, and the multisubject CSP. Evaluations on three BCI competition datasets show that the regularized CSP algorithms outperform other baselines, especially for the high-dimensional small training set. The extensive results validate the efficiency and effectiveness of the proposed CSP formulation in different learning contexts.
AB - Common spatial pattern (CSP) is one of the most successful feature extraction algorithms for brain-computer interfaces (BCIs). It aims to find spatial filters that maximize the projected variance ratio between the covariance matrices of the multichannel electroencephalography (EEG) signals corresponding to two mental tasks, which can be formulated as a generalized eigenvalue problem (GEP). However, it is challenging in principle to impose additional regularization onto the CSP to obtain structural solutions (e.g., sparse CSP) due to the intrinsic nonconvexity and invariance property of GEPs. This article reformulates the CSP as a constrained minimization problem and establishes the equivalence of the reformulated and the original CSPs. An efficient algorithm is proposed to solve this optimization problem by alternately performing singular value decomposition (SVD) and least squares. Under this new formulation, various regularization techniques for linear regression can then be easily implemented to regularize the CSPs for different learning paradigms, such as the sparse CSP, the transfer CSP, and the multisubject CSP. Evaluations on three BCI competition datasets show that the regularized CSP algorithms outperform other baselines, especially for the high-dimensional small training set. The extensive results validate the efficiency and effectiveness of the proposed CSP formulation in different learning contexts.
KW - Brain-computer interface (BCI)
KW - common spatial pattern (CSP)
KW - generalized eigenvalue problem (GEP)
KW - least squares
KW - multitask learning
KW - singular value decomposition (SVD)
KW - sparse learning
KW - transfer learning
UR - http://www.scopus.com/inward/record.url?scp=85112147488&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85112147488&partnerID=8YFLogxK
U2 - 10.1109/TCYB.2020.2982901
DO - 10.1109/TCYB.2020.2982901
M3 - Article
C2 - 32324587
AN - SCOPUS:85112147488
SN - 2168-2267
VL - 51
SP - 5008
EP - 5020
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
IS - 10
ER -