A survey of kernel and spectral methods for clustering

Maurizio Filippone*, Francesco Camastra, Francesco Masulli, Stefano Rovetta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

676 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)176-190
Number of pages15
JournalPattern Recognition
Issue number1
StatePublished - Jan 2008


  • Kernel clustering
  • Kernel fuzzy clustering
  • Mercer kernels
  • Partitional clustering
  • Spectral clustering

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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