Extension of the semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalization to the efficient calculation of coupled CP decompositions

Abstract

Several combined signal processing applications such as the joint processing of EEG and MEG data can benefit from coupled tensor decompositions, for instance, the coupled CP (Canonical Polyadic) decomposition. The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. The SECSI (Semi-Algebraic framework for approximate CP decomposition via SImultaneaous matrix diagonalization) framework is an efficient tool for the calculation of the CP decomposition based on matrix diagonalizations. It provides a semi-algebraic solution for the CP decomposition even in ill-posed scenarios, e.g., if the columns of a factor matrix are highly correlated. Moreover, the SECSI framework provides an adjustable complexity-accuracy trade-off. In this paper, we present an extension of the SECSI framework to the efficient calculation of coupled CP decompositions and show its advantages compared to the traditional solution via alternating least squares (ALS) and other state of the art algorithms.