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  Input space versus feature space in kernel-based methods

Schölkopf, B., Mika, S., Burges, C., Knirsch, P., Müller, K.-R., Rätsch, G., et al. (1999). Input space versus feature space in kernel-based methods. IEEE Transactions on Neural Networks, 10(5), 1000-1017. doi:10.1109/72.788641.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-E655-6 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-BF89-A
Genre: Journal Article

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 Creators:
Schölkopf, B, Author              
Mika, S, Author
Burges, CJC, Author
Knirsch, P1, 2, Author              
Müller, K-R, Author              
Rätsch, G, Author              
Smola, AJ, Author              
Affiliations:
1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              

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 Abstract: This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods. Following this, we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel, using the example of the class of inhomogeneous polynomial kernels, which are often used in SV pattern recognition. We then discuss the connection between feature space and input space by dealing with the question of how one can, given some vector in feature space, find a preimage (exact or approximate) in input space. We describe algorithms to tackle this issue, and show their utility in two applications of kernel methods. First, we use it to reduce the computational complexity of SV decision functions; second, we combine it with the kernel PCA algorithm, thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real-world data.

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 Dates: 1999-09
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1109/72.788641
BibTex Citekey: 216
 Degree: -

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Title: IEEE Transactions on Neural Networks
Source Genre: Journal
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Publ. Info: New York, NY : Institute of Electrical and Electronics Engineers
Pages: - Volume / Issue: 10 (5) Sequence Number: - Start / End Page: 1000 - 1017 Identifier: ISSN: 1045-9227
CoNE: https://pure.mpg.de/cone/journals/resource/954925591430