Motor Imagery Classification Based on Bilinear Sub-Manifold Learning of Symmetric Positive-Definite Matrices

Xiaofeng Xie, Zhu Liang Yu*, Haiping LU, Zhenghui Gu, Yuanqing Li

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

87 Citations (Scopus)


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.

Original languageEnglish
Article number7506082
Pages (from-to)504-516
Number of pages13
JournalIEEE Transactions on Neural Systems and Rehabilitation Engineering
Issue number6
Publication statusPublished - Jun 2017

Scopus Subject Areas

  • Internal Medicine
  • Neuroscience(all)
  • Biomedical Engineering

User-Defined Keywords

  • Classification algorithms
  • covariance matrices
  • dimensionality reduction
  • electroencephalography (EEG)
  • information geometry
  • motor imagery


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