Abstract

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-$(L_{r,n}, L_{r,n}, 1)$ terms. Finally, numerical experiments demonstrate that linear algebra based algorithms can provide good results at a reasonable computational cost.

Code description

This package provides experiment files and auxiliary files for the coupled CPD and LL1 paper.

Reference

M. Sørensen, L. De Lathauwer, "Coupled canonical polyadic decompositions and (coupled) decompositions in multilinear rank-$(L_{r,n}, L_{r,n}, 1)$ terms — Part II: Algorithms," SIAM Journal on Matrix Analysis and Applications, vol. 36, no. 3, pp. 1015-1045, July 2015.

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