Feature space perspectives for learning the kernel

Authors:
Charles A. Micchelli;Massimiliano Pontil
Affiliations:
Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, USA 12222;Department of Computer Science, University College London, London, England, UK WC1E
Venue:
Machine Learning
Year:
2007

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Abstract

In this paper, we continue our study of learning an optimal kernel in a prescribed convex set of kernels (Micchelli & Pontil, 2005) . We present a reformulation of this problem within a feature space environment. This leads us to study regularization in the dual space of all continuous functions on a compact domain with values in a Hilbert space with a mix norm. We also relate this problem in a special case to $${\cal L}^p$$ regularization.