An effective way of jointly analyzing data from multiple sources is through coupled matrix and tensor factorizations (CMTF). Different characteristics of datasets from multiple sources require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. While existing algorithmic approaches for CMTF can incorporate constraints, linear couplings and different loss functions, none of them has been shown to achieve the flexibility to incorporate all. We propose a flexible algorithmic framework for coupled matrix and tensor factorizations, which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations. Numerical experiments on simulated datasets and real data from chemometrics and hyperspectral super-resolution demonstrate that the proposed approach is accurate, flexible and computationally efficient with comparable or better performance than available CMTF algorithms.

While we focus on CANDECOMP/PARAFAC (CP) –based CMTF models, we will also briefly discuss the use of an AO-ADMM based algorithmic approach for fitting a PARAFAC2 model.  We demonstrate that the proposed algorithmic approach enables imposing constraints in all modes, which has been a challenge using the traditional alternating least squares-based algorithm used for PARAFAC2.