The Pre-Image Problem in Kernel Methods

James T. Kwok; Ivor W. Tsang

The Pre-Image Problem in Kernel Methods

James T. Kwok^*
, Ivor W. Tsang

^*Corresponding author for this work

Department of Computer Science and Engineering

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

55 Citations (Scopus)

Abstract

In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.

Original language	English
Title of host publication	Proceedings, Twentieth International Conference on Machine Learning
Editors	T. Fawcett, N. Mishra
Pages	408-415
Number of pages	8
Publication status	Published - 2003
Event	Proceedings, Twentieth International Conference on Machine Learning - Washington, DC, United States Duration: 21 Aug 2003 → 24 Aug 2003

Publication series

Name	Proceedings, Twentieth International Conference on Machine Learning
Volume	1

Conference

Conference	Proceedings, Twentieth International Conference on Machine Learning
Country/Territory	United States
City	Washington, DC
Period	21/08/03 → 24/08/03

Cite this

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title = "The Pre-Image Problem in Kernel Methods",

abstract = "In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.",

author = "Kwok, \{James T.\} and Tsang, \{Ivor W.\}",

year = "2003",

language = "English",

isbn = "1577351894",

series = "Proceedings, Twentieth International Conference on Machine Learning",

pages = "408--415",

editor = "T. Fawcett and N. Mishra",

booktitle = "Proceedings, Twentieth International Conference on Machine Learning",

note = "Proceedings, Twentieth International Conference on Machine Learning ; Conference date: 21-08-2003 Through 24-08-2003",

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The Pre-Image Problem in Kernel Methods. / Kwok, James T.; Tsang, Ivor W.
Proceedings, Twentieth International Conference on Machine Learning. ed. / T. Fawcett; N. Mishra. 2003. p. 408-415 (Proceedings, Twentieth International Conference on Machine Learning; Vol. 1).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

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AU - Tsang, Ivor W.

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N2 - In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.

AB - In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.

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M3 - Conference Paper published in a book

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SN - 1577351894

T3 - Proceedings, Twentieth International Conference on Machine Learning

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BT - Proceedings, Twentieth International Conference on Machine Learning

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Y2 - 21 August 2003 through 24 August 2003

ER -

The Pre-Image Problem in Kernel Methods

Abstract

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