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Conference Paper

Learning to Find Pre-Images

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83791

Bakir,  GH
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84311

Weston,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Bakir, G., Weston, J., & Schölkopf, B. (2004). Learning to Find Pre-Images. Advances in Neural Information Processing Systems, 449-456.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D8ED-0
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.