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On Spectral Learning

Argyriou, A; Micchelli, CA; Pontil, M; (2010) On Spectral Learning. J MACH LEARN RES , 11 935 - 953. Gold open access


In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W. Instances of this problem in machine learning include multi-task learning, collaborative filtering and multi-view learning, among others. Our goal is to elucidate the form of the optimal solution of spectral learning. The theory of spectral learning relies on the von Neumann characterization of orthogonally invariant norms and their association with symmetric gauge functions. Using this tool we formulate a representer theorem for spectral regularization and specify it to several useful example, such as Schatten p-norms, trace norm and spectral norm, which should proved useful in applications.

Type: Article
Title: On Spectral Learning
Open access status: An open access publication
Publisher version: http://www.jmlr.org/
Keywords: kernel methods, matrix learning, minimal norm interpolation, multi-task learning, orthogonally invariant norms, regularization
UCL classification: UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
URI: http://discovery.ucl.ac.uk/id/eprint/163470
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