TY - JOUR
T1 - Motor Imagery Classification Based on Bilinear Sub-Manifold Learning of Symmetric Positive-Definite Matrices
AU - Xie, Xiaofeng
AU - Yu, Zhu Liang
AU - Lu, Haiping
AU - Gu, Zhenghui
AU - Li, Yuanqing
N1 - Funding Information:
This work was supported in part by the National Key Basic Research Program of China (973 Program) under Grant 2015CB351703, the National Natural Science Foundation of China under Grants 61573150, 61573152, 61175114 and 91420302, the Natural Science Foundation of Guangdong under Grants 2013KJCX0009, 2014A030312005, 2014A030313253.
PY - 2017/6
Y1 - 2017/6
N2 - In motor imagery brain-computer interfaces (BCIs), the symmetric positive-definite (SPD) covariance matrices of electroencephalogram (EEG) signals carry important discriminative information. In this paper, we intend to classify motor imagery EEG signals by exploiting the fact that the space of SPD matrices endowed with Riemannian distance is a high-dimensional Riemannian manifold. To alleviate the overfitting and heavy computation problems associated with conventional classification methods on high-dimensional manifold, we propose a framework for intrinsic sub-manifold learning from a high-dimensional Riemannian manifold. Considering a special case of SPD space, a simple yet efficient bilinear sub-manifold learning (BSML) algorithm is derived to learn the intrinsic sub-manifold by identifying a bilinear mapping that maximizes the preservation of the local geometry and global structure of the original manifold. Two BSML-based classification algorithms are further proposed to classify the data on a learned intrinsic sub-manifold. Experimental evaluation of the classification of EEG revealed that the BSML method extracts the intrinsic sub-manifold approximately 5× faster and with higher classification accuracy compared with competing algorithms. The BSML also exhibited strong robustness against a small training dataset, which often occurs in BCI studies.
AB - In motor imagery brain-computer interfaces (BCIs), the symmetric positive-definite (SPD) covariance matrices of electroencephalogram (EEG) signals carry important discriminative information. In this paper, we intend to classify motor imagery EEG signals by exploiting the fact that the space of SPD matrices endowed with Riemannian distance is a high-dimensional Riemannian manifold. To alleviate the overfitting and heavy computation problems associated with conventional classification methods on high-dimensional manifold, we propose a framework for intrinsic sub-manifold learning from a high-dimensional Riemannian manifold. Considering a special case of SPD space, a simple yet efficient bilinear sub-manifold learning (BSML) algorithm is derived to learn the intrinsic sub-manifold by identifying a bilinear mapping that maximizes the preservation of the local geometry and global structure of the original manifold. Two BSML-based classification algorithms are further proposed to classify the data on a learned intrinsic sub-manifold. Experimental evaluation of the classification of EEG revealed that the BSML method extracts the intrinsic sub-manifold approximately 5× faster and with higher classification accuracy compared with competing algorithms. The BSML also exhibited strong robustness against a small training dataset, which often occurs in BCI studies.
KW - Classification algorithms
KW - covariance matrices
KW - dimensionality reduction
KW - electroencephalography (EEG)
KW - information geometry
KW - motor imagery
UR - http://www.scopus.com/inward/record.url?scp=85021335625&partnerID=8YFLogxK
U2 - 10.1109/TNSRE.2016.2587939
DO - 10.1109/TNSRE.2016.2587939
M3 - Journal article
C2 - 27392361
AN - SCOPUS:85021335625
SN - 1534-4320
VL - 25
SP - 504
EP - 516
JO - IEEE Transactions on Neural Systems and Rehabilitation Engineering
JF - IEEE Transactions on Neural Systems and Rehabilitation Engineering
IS - 6
M1 - 7506082
ER -