Clustering via Kernel Decomposition

Anna Szynkowiak Have; Mark A. Girolami; Jan Larsen

doi:10.1109/TNN.2005.860840

Clustering via Kernel Decomposition

Anna Szynkowiak Have, Mark A. Girolami, Jan Larsen

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Abstract

Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets.

Original language	English
Journal	I E E E Transactions on Neural Networks
Volume	17
Issue number	1
Pages (from-to)	256-264
ISSN	1045-9227
DOIs	https://doi.org/10.1109/TNN.2005.860840
Publication status	Published - 2006

Bibliographical note

Copyright: 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

Keywords

probabilistic clustering
aggregated Markov models
spectral clustering
kernel principal component analysis
kernel decomposition

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AU - Larsen, Jan

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N2 - Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets.

AB - Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets.

KW - probabilistic clustering

KW - aggregated Markov models

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KW - kernel principal component analysis

KW - kernel decomposition

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JO - I E E E Transactions on Neural Networks

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Clustering via Kernel Decomposition

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Keywords

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