Learning to Find Pre-Images

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.

• Type: Conference
• Year: 2003
• Where: NIPS
• Authors: Gökhan H. Bakir, Jason Weston, Bernhard Schölkopf
• Keywords: Input Spaces, Kernel Principal Component Analysis, NIPS 2003, NIPS 2007, Reproducing Kernel Hilbert Space