Distributed Elastic Net Regularized Blind Compressive Sensing for Recommender System Design

Design of recommender system following the latent factor model is widely cast as a matrix factorization problem yielding a rating matrix, which is a product of a dense user and a dense item factor matrices. A dense user factor matrix is a credible assumption as all users are expected to have some degree of affinity towards all the latent factors. However, for items it’s not a reasonable supposition as no item is expected to possess all the traits (factors). In this work, we propose a matrix factorization model which yields a dense user but a sparse item factor matrix; having equivalence to Blind Compressive Sensing (BCS) formulation. Basic BCS framework is augmented with an added elastic net regularization term. The addition helps in capturing correlation between different item latent factors. Despite the efficiency of matrix factorization approach, it’s not feasible to apply the techniques for very large datasets (rating matrices). For this purpose, we employ Divide and Combine (DnC) approach – wherein proposed method is applied to distinct subsets of the rating matrix simultaneously and resulting estimates combined to yield the final result. The (randomized) DnC approach retains the convergence guarantees of matrix factorization. Experiments were conducted on real world Movielens dataset and our technique was compared against popular matrix factorization methods. The results indicate the superiority of our method in terms of both accuracy and speed.