Learning to Find Pre-Images
Goekhan BakIr, Jason Weston and Bernhard Schölkopf
In: NIPS 16, Vancouver(2004).
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.