  The increasing availability of implicit feedback datasets has raised the
interest in developing effective collaborative filtering techniques able to
deal asymmetrically with unambiguous positive feedback and ambiguous negative
feedback. In this paper, we propose a principled kernel-based collaborative
filtering method for top-N item recommendation with implicit feedback. We
present an efficient implementation using the linear kernel, and we show how to
generalize it to kernels of the dot product family preserving the efficiency.
We also investigate on the elements which influence the sparsity of a standard
cosine kernel. This analysis shows that the sparsity of the kernel strongly
depends on the properties of the dataset, in particular on the long tail
distribution. We compare our method with state-of-the-art algorithms achieving
good results both in terms of efficiency and effectiveness.
