  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 achieve 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. Recent analysis show 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 arity 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.
