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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.
@inproceedings{2281, title = {Learning to Find Pre-Images}, journal = {Advances in Neural Information Processing Systems}, booktitle = {Advances in Neural Information Processing Systems 16}, 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.}, pages = {449-456}, editors = {S Thrun and LK Saul and B Sch{\"o}lkopf}, publisher = {MIT Press}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, address = {Cambridge, MA, USA}, month = jun, year = {2004}, slug = {2281}, author = {Bakir, GH. and Weston, J. and Sch{\"o}lkopf, B.}, month_numeric = {6} }