A survey of kernel and spectral methods for clustering

Authors:
Maurizio Filippone;Francesco Camastra;Francesco Masulli;Stefano Rovetta
Affiliations:
Department of Computer and Information Science, University of Genova, and CNISM, Via Dodecaneso 35, I 16146 Genova, Italy;Department of Applied Science, University of Naples Parthenope, Via A. De Gasperi 5, I 80133 Napoli, Italy;Department of Computer and Information Science, University of Genova, and CNISM, Via Dodecaneso 35, I 16146 Genova, Italy;Department of Computer and Information Science, University of Genova, and CNISM, Via Dodecaneso 35, I 16146 Genova, Italy
Venue:
Pattern Recognition
Year:
2008

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Abstract

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm.