Author:

Keywords:

SISTA, BIOTENSORS - 339804;info:eu-repo/grantAgreement/EC/FP7/339804, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, coupled decompositions, higher-order tensor, polyadic decomposition, parallel factor, canonical decomposition, canonical polyadic decomposition, coupled matrix-tensor factorization, HIGHER-ORDER TENSORS, L-R, UNIQUENESS, MATRIX, APPROXIMATION, REDUCTION, ALGEBRA, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics

Abstract:

© 2015 Society for Industrial and Applied Mathematics. The coupled canonical polyadic decomposition (CPD) is an emerging tool for the joint analysis of multiple data sets in signal processing and statistics. Despite their importance, linear algebra based algorithms for coupled CPDs have not yet been developed. In this paper, we first explain how to obtain a coupled CPD from one of the individual CPDs. Next, we present an algorithm that directly takes the coupling between several CPDs into account. We extend the methods to single and coupled decompositions in multilinear rank-(Lr,n, Lr,n, 1) terms. Finally, numerical experiments demonstrate that linear algebra based algorithms can provide good results at a reasonable computational cost.