PARAFAC2-based Coupled Matrix and Tensor Factorizations
This work addresses data fusion challenges for researchers analyzing irregular tensors, though it is incremental as it builds on prior PARAFAC2 and CMTF methods.
The paper tackles the limitations of existing PARAFAC2-based coupled matrix and tensor factorization models by proposing a new algorithmic framework that supports various constraints and linear couplings, demonstrating accurate recovery of underlying patterns in numerical experiments.
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.