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IEEE Trans Pattern Anal Mach Intell. 2010 Feb;32(2):335-47. doi: 10.1109/TPAMI.2008.292.

Multiway spectral clustering with out-of-sample extensions through weighted kernel PCA.

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  • 1Department of Electrical Engineering ESATSCD-SISTA, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Heverlee, Leuven, Belgium. carlos.alzate@esat.kuleuven.be

Abstract

A new formulation for multiway spectral clustering is proposed. This method corresponds to a weighted kernel principal component analysis (PCA) approach based on primal-dual least-squares support vector machine (LS-SVM) formulations. The formulation allows the extension to out-of-sample points. In this way, the proposed clustering model can be trained, validated, and tested. The clustering information is contained on the eigendecomposition of a modified similarity matrix derived from the data. This eigenvalue problem corresponds to the dual solution of a primal optimization problem formulated in a high-dimensional feature space. A model selection criterion called the Balanced Line Fit (BLF) is also proposed. This criterion is based on the out-of-sample extension and exploits the structure of the eigenvectors and the corresponding projections when the clusters are well formed. The BLF criterion can be used to obtain clustering parameters in a learning framework. Experimental results with difficult toy problems and image segmentation show improved performance in terms of generalization to new samples and computation times.

PMID:
20075462
[PubMed]
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