Combining Swarm with Gradient Search for Maximum Margin Matrix Factorization

Maximum Margin Matrix Factorization is one of the very popular techniques of collaborative filtering. The discrete valued rating matrix with a small portion of known ratings is factorized into two latent factors and the unknown ratings are estimated by the resulting product of the factors. The factorization is achieved by optimizing a loss function and the optimization is carried out by gradient descent or its variants. It is observed that any of these algorithms yields near-global optimizing point irrespective of the initial seed point. In this paper, we propose to combine swarm-like search with gradient descent search. Our algorithm starts from multiple initial points and uses gradient information and swarm-search as the search progresses. We show that by this process we get an efficient search scheme to get near optimal point for maximum margin matrix factorization.