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Abstract

We consider the problem of reconstructing patterns from a feature map. Learning algorithms using kernels to operate in a reproducing kernel Hilbert space (RKHS) express their solutions in terms of input points mapped into the RKHS. We
introduce a technique based on kernel principal component analysis and regression to reconstruct corresponding patterns in the input space (aka pre-images) and review its performance in several applications requiring the construction of pre-images. The introduced technique avoids
difficult and/or unstable numerical optimization, is easy to
implement and, unlike previous methods, permits the computation of pre-images in discrete input spaces.