Boolean kernels for collaborative filtering in top-N item recommendation

In many personalized recommendation problems available data consists only of positive interactions (implicit feedback) between users and items. This problem is also known as One-Class Collaborative Filtering (OC-CF). Linear models usually achieves state-of-the-art performances on OC-CF problems and many efforts have been devoted to build more expressive and complex representations able to improve the recommendations but with no much success. Recent analysis shows that collaborative filtering (CF) datasets have peculiar characteristics such as high sparsity and a long tailed distribution of the ratings. In this paper we propose a boolean kernel, called Disjunctive Kernel, which is less expressive than the linear one but it is able to alleviate the sparsity issue in CF contexts. The embedding of this kernel is composed by all the combinations of a certain degree d of the input variables, and these combined features are semantically interpreted as disjunctions of the input variables. Experiments on several CF datasets show the effectiveness and the efficiency of the proposed kernel.