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

AbstractIn this paper we review a multilinear generalization of the singular value decomposition and the best rank-(R1,R2,…,RN) 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