Kernel PCA and de-noising in feature spaces

Sebastian Mika, Bernhard Schölkopf, Alex Smola, Klaus Muller, Matthias Scholz, Gunnar Rätsch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

575 Citations (Scopus)

Abstract

Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
Pages536-542
Number of pages7
ISBN (Print)0262112450, 9780262112451
Publication statusPublished - 1999 Jan 1
Externally publishedYes
Event12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United States
Duration: 1998 Nov 301998 Dec 5

Other

Other12th Annual Conference on Neural Information Processing Systems, NIPS 1998
CountryUnited States
CityDenver, CO
Period98/11/3098/12/5

Fingerprint

Data compression
Principal component analysis

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Mika, S., Schölkopf, B., Smola, A., Muller, K., Scholz, M., & Rätsch, G. (1999). Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems (pp. 536-542). Neural information processing systems foundation.

Kernel PCA and de-noising in feature spaces. / Mika, Sebastian; Schölkopf, Bernhard; Smola, Alex; Muller, Klaus; Scholz, Matthias; Rätsch, Gunnar.

Advances in Neural Information Processing Systems. Neural information processing systems foundation, 1999. p. 536-542.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mika, S, Schölkopf, B, Smola, A, Muller, K, Scholz, M & Rätsch, G 1999, Kernel PCA and de-noising in feature spaces. in Advances in Neural Information Processing Systems. Neural information processing systems foundation, pp. 536-542, 12th Annual Conference on Neural Information Processing Systems, NIPS 1998, Denver, CO, United States, 98/11/30.
Mika S, Schölkopf B, Smola A, Muller K, Scholz M, Rätsch G. Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems. Neural information processing systems foundation. 1999. p. 536-542
Mika, Sebastian ; Schölkopf, Bernhard ; Smola, Alex ; Muller, Klaus ; Scholz, Matthias ; Rätsch, Gunnar. / Kernel PCA and de-noising in feature spaces. Advances in Neural Information Processing Systems. Neural information processing systems foundation, 1999. pp. 536-542
@inproceedings{4cd4105e9ef64787977649701b1c5c07,
title = "Kernel PCA and de-noising in feature spaces",
abstract = "Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.",
author = "Sebastian Mika and Bernhard Sch{\"o}lkopf and Alex Smola and Klaus Muller and Matthias Scholz and Gunnar R{\"a}tsch",
year = "1999",
month = "1",
day = "1",
language = "English",
isbn = "0262112450",
pages = "536--542",
booktitle = "Advances in Neural Information Processing Systems",
publisher = "Neural information processing systems foundation",

}

TY - GEN

T1 - Kernel PCA and de-noising in feature spaces

AU - Mika, Sebastian

AU - Schölkopf, Bernhard

AU - Smola, Alex

AU - Muller, Klaus

AU - Scholz, Matthias

AU - Rätsch, Gunnar

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.

AB - Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.

UR - http://www.scopus.com/inward/record.url?scp=84898970836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898970836&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898970836

SN - 0262112450

SN - 9780262112451

SP - 536

EP - 542

BT - Advances in Neural Information Processing Systems

PB - Neural information processing systems foundation

ER -