Blind Compressive Sensing Framework for Collaborative Filtering

Existing works based on latent factor models have focused on representing the rating matrix as a product of user and item latent factor matrices, both being dense. Latent (factor) vectors define the degree to which a trait is possessed by an item or the affinity of user towards that trait. A dense user matrix is a reasonable assumption as each user will like/dislike a trait to certain extent. However, any item will possess only a few of the attributes and never all. Hence, the item matrix should ideally have a sparse structure rather than a dense one as formulated in earlier works. Therefore we propose to factor the ratings matrix into a dense user matrix and a sparse item matrix which leads us to the Blind Compressed Sensing (BCS) framework. We derive an efficient algorithm for solving the BCS problem based on Majorization Minimization (MM) technique. Our proposed approach is able to achieve significantly higher accuracy and shorter run times as compared to existing approaches.