PARAFAC2-based Coupled Matrix and Tensor Factorizations with Constraints

TL;DR

This paper introduces a flexible algorithmic framework for PARAFAC2-based coupled matrix and tensor factorizations, enabling various constraints and couplings, improving accuracy and efficiency over existing methods.

Contribution

It presents a novel, versatile framework using AO and ADMM for PARAFAC2-based CMTF models with constraints and couplings, addressing previous limitations.

Findings

Enhanced modeling of irregular tensors and dynamic data.

Improved accuracy and efficiency compared to state-of-the-art methods.

Demonstrated utility on simulated and real datasets.

Abstract

Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear CANDECOMP/PARAFAC (CP) tensor model, recently also the more flexible PARAFAC2 model has been integrated into CMTF models. PARAFAC2 tensor models can handle irregular/ragged tensors and have shown to be especially useful for modelling dynamic data with unaligned or irregular time profiles. However, existing PARAFAC2-based CMTF models have limitations in terms of possible regularizations on the factors and/or types of coupling between datasets. To address these limitations, in this paper we introduce a flexible algorithmic framework that fits PARAFAC2-based CMTF models using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The proposed framework allows to impose various constraints on all modes and linear couplings to other matrix-, CP- or PARAFAC2-models. Experiments on various simulated and a real dataset demonstrate the utility and versatility of the proposed framework as well as its benefits in terms of accuracy and efficiency in comparison with state-of-the-art methods.