Vector field learning via spectral filtering

Authors:
Luca Baldassarre;Lorenzo Rosasco;Annalisa Barla;Alessandro Verri
Affiliations:
Università degli Studi di Genova, DISI, Genova, Italy;Istituto Italiano di Tecnologia, Genova, Italy and CBCL, Massachusetts Institute of Technology, Cambridge, MA;Università degli Studi di Genova, DISI, Genova, Italy;Università degli Studi di Genova, DISI, Genova, Italy
Venue:
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Year:
2010

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Abstract

In this paper we present and study a new class of regularized kernel methods for learning vector fields, which are based on filtering the spectrum of the kernel matrix. These methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector valued extensions of L2-Boosting. Our theoretical and experimental analysis shows that spectral filters that yield iterative algorithms, such as L2-Boosting, are much faster than Tikhonov regularization and attain the same prediction performances. Finite sample bounds for the different filters can be derived in a common framework and highlight different theoretical properties of the methods. The theory of vector valued reproducing kernel Hilbert space is a key tool in our study.