NLS Algorithm for Kronecker-Structured Linear Systems with a CPD Constrained Solution

Abstract

In various applications within signal processing, system identification, pattern recognition, and scientific computing, the canonical polyadic decomposition (CPD) of a higherorder tensor is only known via general linear measurements. In this paper, we show that the computation of such a CPD can be reformulated as a sum of CPDs with linearly constrained factor matrices by assuming that the measurement matrix can be approximated by a sum of a (small) number of Kronecker products. By properly exploiting the hypothesized structure, we can derive an efficient non-linear least squares algorithm, allowing us to tackle large-scale problems.