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 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

Recommender Systems by means of Information Retrieval

In this paper we present a method for reformulating the Recommender Systems problem in an Information Retrieval one. In our tests we have a dataset of users who give ratings for some movies; we hide some values from the dataset, and we try to predict them again using its remaining portion (the so-called "leave-n-out approach"). In order to use an Information Retrieval algorithm, we reformulate this Recommender Systems problem in this way: a user corresponds to a document, a movie corresponds to a term, the active user (whose rating we want to predict) plays the role of the query, and the ratings are used as weigths, in place of the weighting schema of the original IR algorithm. The output is the ranking list of the documents ("users") relevant for the query ("active user"). We use the ratings of these users, weighted according to the rank, to predict the rating of the active user. We carry out the comparison by means of a typical metric, namely the accuracy of the predictions returned by the algorithm, and we compare this to the real ratings from users. In our first tests, we use two different Information Retrieval algorithms: LSPR, a recently proposed model based on Discrete Fourier Transform, and a simple vector space model