DESICOM as Metaheuristic Search

Decomposition into Simple Components (DESICOM) is a constrained matrix factorization method to decompose asymmetric comparability 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 local optimal solutions. Aiming at computing optimal basis matrices, in this work we show how we will cast the problem of finding optimal basis matrices for DESICOM as metaheuristic search and present an algorithm to factorize asymmetric data matrices. We evaluate our algorithms on synthetic datasets and show that it can find interpretable results and can better escape the locally optimal solutions.