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.
| Author(s): | Bakir, GH. and Weston, J. and Schölkopf, B. |
| Book Title: | Advances in Neural Information Processing Systems 16 |
| Journal: | Advances in Neural Information Processing Systems |
| Pages: | 449-456 |
| Year: | 2004 |
| Month: | June |
| Day: | 0 |
| Editors: | S Thrun and LK Saul and B Sch{\"o}lkopf |
| Publisher: | MIT Press |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Cambridge, MA, USA |
| Event Name: | 17th Annual Conference on Neural Information Processing Systems (NIPS 2003) |
| Event Place: | Vancouver, BC, Canada |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| ISBN: | 0-262-20152-6 |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@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}
}