Regularized LDA based on separable scatter matrices for classification of spatio-spectral EEG patterns

Linear discriminant analysis (LDA) is a commonly-used feature extraction technique. For matrix-variate data such as spatio-spectral electroencephalogram (EEG), matrix-variate LDA formulations have been proposed. Compared to the standard vector-variate LDA, these formulations assume a separable structure for the within-class and between-class scatter matrices; these structured parameters can be estimated more accurately with a limited number of training samples. However, separable scatters do not fit some data, resulting in aggravated performance for matrix-variate methods. This paper first proposes a common framework for the vector-variate LDA with non-separable scatters and our previously proposed solution with separable scatters. Then, a regularization of the non-separable scatter estimates toward the separable estimates is introduced. This novel regularized framework integrates vector-variate and matrix-variate approaches, and allows the estimated scatter matrices to adapt to the data characteristics. Experiments on data set V from BCI competition III demonstrate that the proposed framework achieves a considerable classification performance gain.