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Thomas Hofmann, Bernhard Schölkopf, and Alexander J Smola (2008)

Kernel Methods in Machine Learning

Annals of Statistics, 36:1171-1220.

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.
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