Interpretable Matrix Factorization with Stochasticity Constrained Nonnegative DEDICOM

Decomposition into Directed Components (DEDICOM) is a special matrix factorization technique to factorize a given asymmetric similarity matrix into a combination of a loading matrix describing the latent structures in the data and an asymmetric affinity matrix encoding the relationships between the found latent structures. Finding DEDICOM factors can be casted as a matrix norm minimization problem that requires alternating least square updates to find appropriate factors. Yet, due to the way DEDICOM reconstructs the data, unconstrained factors might yield results that are difficult to interpret. In this paper we derive a projection-free gradient descent based alternating least squares algorithm to calculate constrained DEDICOM factors. Our algorithm constrains the loading matrix to be column-stochastic and the affinity matrix to be nonnegative for more interpretable low rank representations. Additionally, unlike most of the available approximate solutions for finding the factors, our approach take into account the entire occurrences of the loading matrix during the optimization process to assure convergence. We evaluate our algorithm on a real world behavioral dataset containing pairwise asymmetric associations between variety of game titles.