A flexible modeling framework for coupled matrix and tensor factorizations

Joint analysis of data from multiple sources has proved useful in many disciplines including metabolomics and social network analysis. However, data fusion remains a challenging task in need of data mining tools that can capture the underlying structures from multi-relational and heterogeneous data sources. In order to address this challenge, data fusion has been formulated as a coupled matrix and tensor factorization (CMTF) problem. Coupled factorization problems have commonly been solved using alternating methods and, recently, unconstrained all-at-once optimization algorithms. In this paper, unlike previous studies, in order to have a flexible modeling framework, we use a general-purpose optimization solver that solves for all factor matrices simultaneously and is capable of handling additional linear/nonlinear constraints with a nonlinear objective function. We formulate CMTF as a constrained optimization problem and develop accurate models more robust to overfactoring. The effectiveness of the proposed modeling/algorithmic framework is demonstrated on simulated and real data.