Nonnegative Tensor Factorization for EEG Pattern Classification

Learning fruitful representation from data is one of fundamental problems in machine learning and pattern recognition. Various methods have been developed, including factor analysis, principal component analysis (PCA), independent component analysis (ICA), manifold learning, and so on. Among those, nonnegative matrix factorization (NMF) has recently drawn extensive attention, since promising results were reported in handling nonnegative data such as document, image data, spectrograms of audio. NMF seeks a decomposition of a nonnegative data matrix into a product of two factor matrices (basis matrix and encoding matrix) such that all factor matrices are forced to be nonnegative. In this talk, I will begin with the useful behavior of NMF in EEG pattern classification, which plays a critical role in noninvasive brain computer interface (BCI). Next, I will introduce multiway extension of NMF, what is called, “nonnegative tensor factorization” and will emphasize its useful behavior in EEG pattern classification. A tensor is nothing but ‘multiway array’, generalizing vector and matrix in order to accommodate higher-order representations. For instance, a vector is a 1-way tensor, a matrix is a 2-way tensor, and a cube is a 3-way tensor, etc. Through this talk, I will stress why tensor is useful in learning fruitful representation, compared to existing matrix-based methods. Proc. of the 8th POSTECH-KYUTECH Joint Workshop on Neuroinformatics, Kitakyushu, Japan, 2008