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

TL;DR

This paper introduces a spectral regularization framework for collaborative filtering that generalizes low-rank matrix completion, allowing the integration of user and object attributes, and unifies various learning methods.

Contribution

It proposes a novel spectral regularization approach for CF that incorporates auxiliary information and provides new estimation algorithms with theoretical guarantees.

Findings

Enhanced CF performance with attribute integration

Unified framework for multi-task learning methods

Demonstrated advantages on standard datasets

Abstract

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.