Kernel methods in machine learning
Abstract
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2007
 DOI:
 10.48550/arXiv.math/0701907
 arXiv:
 arXiv:math/0701907
 Bibcode:
 2007math......1907H
 Keywords:

 Mathematics  Statistics;
 Mathematics  Probability;
 30C40 (Primary) 68T05 (Secondary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)