Deep maximum margin matrix factorization

Collaborative filtering (CF) over ordinal feedback is naturally organized as a problem of matrix completion, where the input consists of a partially observed user-item interaction matrix. Maximum Margin Matrix Factorization (MMMF) has achieved widespread popularity for effectively completing such partially observed ordinal matrices from its inception. Geometrically, MMMF embeds items as points and users as linear hyperplanes, separating items with similar ratings from others. The all-threshold hinge loss function ensures that the user hyperplane maximizes the margin between distinct classes of rated items. However, the restriction that the user hyperplane be linear limits the performance of MMMF substantially, as user features are often intricate and do not exhibit linear patterns. To address this, we have proposed a deep variant of maximum margin matrix factorization that can easily predict user-item interactions by accommodating complex, non-linear user tastes and item feature representations. We have experimentally shown over the three benchmark datasets that the proposed deep variant of MMMF outperforms various state-of-the-art CF methods in terms of the Normalized Mean Absolute Error (NMAE) metric.