We present a general approach for collaborative filtering (CF) using spectral
regularization to learn linear operators from "users" to the "objects" they
rate. Recent low-rank type matrix completion approaches to CF are shown to be
special cases. However, unlike existing regularization based CF methods, our
approach can be used to also incorporate information such as attributes of the
users or the objects -- a limitation of existing regularization based CF
methods. We then provide novel representer theorems that we use to develop new
estimation methods. We provide learning algorithms based on low-rank
decompositions, and test them on a standard CF dataset. The experiments
indicate the advantages of generalizing the existing regularization based CF
methods to incorporate related information about users and objects. Finally, we
show that certain multi-task learning methods can be also seen as special cases
of our proposed approach
