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Abstract

The last years have witnessed an increasing interest in Support Vector (SV) machines, which use Mercer kernels for efficiently performing computations in high-dimensional spaces. In pattern recognition, the SV algorithm constructs nonlinear decision functions by training a classifier to perform a linear separation in some high-dimensional space which is nonlinearly related to input space. Recently, we have developed a technique for Nonlinear Principal Component Analysis (Kernel PCA) based on the same types of kernels. This way, we can for instance efficiently extract polynomial features of arbitrary order by computing projections onto principal components in the space of all products of n pixels of images. We explain the idea of Mercer kernels and associated feature spaces, and describe connections to the theory of reproducing kernels and to regularization theory, followed by an overview of the above algorithms employing these kernels.