A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings
This work addresses data fusion problems in multi-source analysis, offering a more flexible tool for researchers and practitioners, though it is incremental as it builds on existing CMTF methods with enhanced adaptability.
The authors tackled the challenge of jointly analyzing multi-source data with varying characteristics by proposing a flexible algorithmic framework for coupled matrix and tensor factorizations that supports diverse regularizations, constraints, loss functions, and linear couplings. The framework demonstrated accurate and computationally efficient performance, matching or surpassing existing methods for Frobenius norm loss and showing effectiveness with Kullback-Leibler divergence on count data.
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.