PARAFAC2-based Coupled Matrix and Tensor Factorizations

TL;DR

This paper introduces a flexible algorithmic framework for PARAFAC2-based coupled matrix and tensor factorizations, enabling advanced data fusion with various constraints and couplings, improving pattern recovery accuracy.

Contribution

It develops a novel algorithmic approach combining AO and ADMM for fitting PARAFAC2-based CMTF models with diverse regularizations and couplings.

Findings

Accurately recovers underlying data patterns.

Supports various regularizations and couplings.

Demonstrates effectiveness through numerical experiments.

Abstract

Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.