Dimensionality reduction in higher-order signal processing and rank-(R1, R2, ..., RN) reduction in multilinear algebra

In this paper we review a multilinear generalization of the singular value decomposition and the best rank-(R-1, R-2,..., R-N) approximation of higher-order tensors. We show that they are important tools for dimensionality reduction in higher-order signal processing. We discuss applications in independent component analysis, simultaneous matrix diagonalization and subspace variants of algorithms based on higher-order statistics. (C) 2004 Elsevier Inc. All rights reserved.