Kernel nonnegative matrix factorization for spectral EEG feature extraction

Nonnegative matrix factorization (NMF) seeks a decomposition of a nonnegative matrix XX0 into a product of two nonnegative factor matrices UX0 and VX0, such that a discrepancy between X and UV> is minimized. Assuming U 1⁄4 XW in the decomposition (for WX0), kernel NMF (KNMF) is easily derived in the framework of least squares optimization. In this paper we make use of KNMF to extract data, which is an important task in EEG classification. Especially when KNMF with linear kernel is used, spectral features are easily computed by a matrix multiplication, while in the standard NMF multiplicative update should be performed repeatedly with the other factor matrix fixed, or the pseudo-inverse of a matrix is required. Moreover in KNMF with linear kernel, one can easily perform feature selection or data selection, because of its sparsity nature. Experiments on two EEG datasets in brain computer interface (BCI) competition indicate the useful behavior of our proposed methods. & 2009 Elsevier B.V. All rights reserved.