DESICOM as Metaheuristic Search

Abstract

Decomposition into Simple Components (DESICOM) is a constrained matrix factorization method to decompose asymmetric square data matrices and represent them as combinations of very sparse basis matrices as well as dense asymmetric affinity matrices. When cast as a least squares problem, the process of finding the factor matrices needs special attention as solving for the basis matrices with fixed affinities is a combinatorial optimization problem usually requiring iterative updates that tend to result in locally optimal solutions. Aiming at computing globally optimal basis matrices, in this work we show how we can cast the problem of finding optimal basis matrices for DESICOM as a metaheuristic search and present an algorithm to factorize asymmetric data matrices. We empirically evaluate our algorithm on synthetic datasets and show that it can not only find interpretable factors but also, compared to the existing approach, can better represent the data and escape locally optimal solutions.

Supported by the Competence Center for Machine Learning Rhine Ruhr (ML2R) which is funded by the Federal Ministry of Education and Research of Germany (grant no. 01|S18038B).