Jason Weston, Bernhard Schölkopf, Gökhan Bakir
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 princi- pal component analysis and regression to reconstruct corresponding pat- terns in the input space (aka pre-images) and review its performance in several applications requiring the construction of pre-images. The intro- duced technique avoids difﬁcult and/or unstable numerical optimization, is easy to implement and, unlike previous methods, permits the compu- tation of pre-images in discrete input spaces.