Missing Data in Kernel {PCA}

Guido Sanguinetti, Neil D. Lawrence
ECML, Berlin, 2006, Springer-Verlag :751-758, 2006.

Abstract

Kernel Principal Component Analysis (KPCA) is a widely used technique for visualisation and feature extraction. Despite its success and flexibility, the lack of a probabilistic interpretation means that some problems, such as handling missing or corrupted data, are very hard to deal with. In this paper we exploit the probabilistic interpretation of linear PCA together with recent results on latent variable models in Gaussian Processes in order to introduce an objective function for KPCA. This in turn allows a principled approach to the missing data problem. Furthermore, this new approach can be extended to reconstruct corrupted test data using fixed kernel feature extractors. The experimental results show strong improvements over widely used heuristics.

Cite this Paper

BibTeX
@InProceedings{Sanguinetti:missingkpca06, title = {Missing Data in Kernel {PCA}}, author = {Sanguinetti, Guido and Lawrence, Neil D.}, booktitle = {ECML, Berlin, 2006}, pages = {751--758}, year = {2006}, series = {Lecture Notes in Computer Science}, address = {Berlin}, publisher = {Springer-Verlag}, pdf = {https://inverseprobability.com/publications/files/CS0608.pdf}, url = {http://inverseprobability.com/publications/sanguinetti-missingkpca06.html}, abstract = {Kernel Principal Component Analysis (KPCA) is a widely used technique for visualisation and feature extraction. Despite its success and flexibility, the lack of a probabilistic interpretation means that some problems, such as handling missing or corrupted data, are very hard to deal with. In this paper we exploit the probabilistic interpretation of linear PCA together with recent results on latent variable models in Gaussian Processes in order to introduce an objective function for KPCA. This in turn allows a principled approach to the missing data problem. Furthermore, this new approach can be extended to reconstruct corrupted test data using fixed kernel feature extractors. The experimental results show strong improvements over widely used heuristics.} }
Endnote
%0 Conference Paper %T Missing Data in Kernel {PCA} %A Guido Sanguinetti %A Neil D. Lawrence %B ECML, Berlin, 2006 %C Lecture Notes in Computer Science %D 2006 %F Sanguinetti:missingkpca06 %I Springer-Verlag %P 751--758 %U http://inverseprobability.com/publications/sanguinetti-missingkpca06.html %X Kernel Principal Component Analysis (KPCA) is a widely used technique for visualisation and feature extraction. Despite its success and flexibility, the lack of a probabilistic interpretation means that some problems, such as handling missing or corrupted data, are very hard to deal with. In this paper we exploit the probabilistic interpretation of linear PCA together with recent results on latent variable models in Gaussian Processes in order to introduce an objective function for KPCA. This in turn allows a principled approach to the missing data problem. Furthermore, this new approach can be extended to reconstruct corrupted test data using fixed kernel feature extractors. The experimental results show strong improvements over widely used heuristics.
RIS
TY - CPAPER TI - Missing Data in Kernel {PCA} AU - Guido Sanguinetti AU - Neil D. Lawrence BT - ECML, Berlin, 2006 DA - 2006/06/19 ID - Sanguinetti:missingkpca06 PB - Springer-Verlag DP - Lecture Notes in Computer Science SP - 751 EP - 758 L1 - https://inverseprobability.com/publications/files/CS0608.pdf UR - http://inverseprobability.com/publications/sanguinetti-missingkpca06.html AB - Kernel Principal Component Analysis (KPCA) is a widely used technique for visualisation and feature extraction. Despite its success and flexibility, the lack of a probabilistic interpretation means that some problems, such as handling missing or corrupted data, are very hard to deal with. In this paper we exploit the probabilistic interpretation of linear PCA together with recent results on latent variable models in Gaussian Processes in order to introduce an objective function for KPCA. This in turn allows a principled approach to the missing data problem. Furthermore, this new approach can be extended to reconstruct corrupted test data using fixed kernel feature extractors. The experimental results show strong improvements over widely used heuristics. ER -
APA
Sanguinetti, G. & Lawrence, N.D.. (2006). Missing Data in Kernel {PCA}. ECML, Berlin, 2006, in Lecture Notes in Computer Science:751-758 Available from http://inverseprobability.com/publications/sanguinetti-missingkpca06.html.

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