Dimensionality reduction for higher-order tensors: algorithms and applications

Abstract

Higher-order tensors have applications in many areas such as biomedical engineering, image processing, and signal processing. For example, dimensionality reduction of a multi-way problem can be achieved by the best rank-(R1,R2,...,RN) approximation of tensors. Contrary to the matrix case, the tensor best rank-(R1,R2,...,RN) approximation cannot be computed in a straightforward way. In this paper, we present the higher-order orthogonal iter- ations and outline two new algorithms, based on the trust-region and conjugate gradient methods on manifolds. We touch on some of the applications.