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bssmolaklausrst gmd de burgesbelllabs com vladresearch att com The last years have witnessed an increasing interest in Support Vector SV machines which use Mercer kernels for eciently performing computations in highdimensional spaces In pattern recognition the SV algorithm constructs nonlinear decision functions by training a classier to perform a linear separation in some highdimensional 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 eciently 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 kernel