Title:

On the best low multilinear rank approximation of higher-order tensors

Abstract:

Higher-order tensors are generalizations of vectors and matrices to third- or even higher-order arrays of numbers. In this talk, we consider a generalization of column and row matrix rank to tensors, called multilinear rank, and discuss the best low multilinear rank approximation problem. Given a higher-order tensor, we are looking for another tensor, as close as possible to the original one and with multilinear rank bounded by prespecified numbers. This approximation is used for dimensionality reduction and signal subspace estimation in higher-order statistics, biomedical signal processing, telecommunications and many other fields. We first consider two particular applications and then briefly present several algorithms for the computation of the approximation. Finally, we point out that the existence of local minima of the associated cost function could cause problems in real applications.