Chapter 11

Learning in Reproducing Kernel Hilbert Spaces

Abstract

This chapter is dedicated to nonparametric modeling of nonlinear functions in reproducing kernel Hilbert spaces (RKHS). The basic definitions and concepts behind RKH spaces are presented, including positive definite kernels, reproducing kernels, kernel matrices, and the kernel trick. Cover’s theorem and the representer theorem are introduced. Then, kernel ridge regression, support vector regression, and support vector machines are studied. Online algorithms for learning in RKH spaces, such as the kernel LMS, NORMA, and the kernel APSM are discussed. The notion of multiple kernel learning is presented and a discussion on sparse modeling for nonparametric models in the context ...

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