Applying the possibilistic c-means algorithm in kernel-induced spaces

Maurizio Filippone*, Francesco Masulli, Stefano Rovetta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In this paper, we study a kernel extension of the classic possibilistic $c$-means. In the proposed extension, we implicitly map input patterns into a possibly high-dimensional space by means of positive semidefinite kernels. In this new space, we model the mapped data by means of the possibilistic clustering algorithm. We study in more detail the special case where we model the mapped data using a single cluster only, since it turns out to have many interesting properties. The modeled memberships in kernel-induced spaces yield a modeling of generic shapes in the input space. We analyze in detail the connections to one-class support vector machines and kernel density estimation, thus, suggesting that the proposed algorithm can be used in many scenarios of unsupervised learning. In the experimental part, we analyze the stability and the accuracy of the proposed algorithm on some synthetic and real datasets. The results show high stability and good performances in terms of accuracy.

Original languageEnglish (US)
Article number5415638
Pages (from-to)572-584
Number of pages13
JournalIEEE Transactions on Fuzzy Systems
Issue number3
StatePublished - Jun 2010


  • Kernel methods
  • Outlier detection
  • Possibilistic clustering
  • Regularization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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