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Abernethy J., Bach F., Evgeniou T., Vert J. (2009). A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization Journal of Machine Learning Research, 10(3), pp. 803-826.
The authors 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, this 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.The authors provide novel representer theorems that we use to develop new estimation methods. The authors then 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, the authors show that certain multi-task learning methods can be also seen as special cases of our proposed approach.