A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization

We present a general approach for collaborative filtering (CF) using spectral regularization to learn linear operators mapping a set of "users" to a set of possibly desired "objects". In particular, several recent low-rank type matrix-completion methods for CF are shown to be special cases of our proposed framework. Unlike existing regularization-based CF, our approach can be used to incorporate additional information such as attributes of the users/objects---a feature currently lacking in existing regularization-based CF approaches---using popular and well-known kernel methods. We provide novel representer theorems that we use to develop new estimation methods. We then provide learning algorithms based on low-rank decompositions and test them on a standard CF data set. 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.