A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

TL;DR

This paper introduces a versatile optimization framework for coupled matrix and tensor factorizations that handles diverse regularizations, constraints, and couplings, improving flexibility and efficiency in multi-source data analysis.

Contribution

The authors develop a flexible algorithmic framework combining AO and ADMM for CMTF, accommodating various regularizations, constraints, and linear couplings seamlessly.

Findings

Accurate and efficient on simulated and real datasets.

Performs comparably or better than existing methods for Frobenius norm loss.

Effective with different loss functions like Kullback-Leibler divergence.

Abstract

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, 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 in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions.