Kernel methods in machine learning

Thomas Hofmann, Bernhard Schölkopf, Alexander J. Smola

The Annals of Statistics · 2008 · Volume 36 · Issue 3

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.

Keywords

30C40, 68T05, graphical models, machine learning, reproducing kernels, Support vector machines

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