On hard and fuzzy c-means clustering with conditionally positive definite kernel

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate three types of c-means clustering algorithms with a conditionally positive definite kernel. One is based on hard c-means, and the others are based on standard and entropy-regularized fuzzy c-means. First, based on a conditionally positive definite kernel describing a squared Euclidean distance between data in the feature space, these algorithms are derived from revised optimization problems of the conventional kernel c-means. Next, based on the relationship between the positive definite kernel and conditionally positive definite kernel, the revised dissimilarity between a datum and a cluster center in the feature space is shown. Finally, it is shown that a conditionally positive definite kernel c-means algorithm and a kernel c-means algorithm with a positive definite kernel derived from the conditionally positive definite kernel are essentially identical to each other. An explicit mapping for a conditionally positive definite kernel is also described geometrically.

Original languageEnglish
Title of host publicationFUZZ 2011 - 2011 IEEE International Conference on Fuzzy Systems - Proceedings
Pages816-820
Number of pages5
DOIs
Publication statusPublished - 2011 Sep 27
Event2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011 - Taipei, Taiwan, Province of China
Duration: 2011 Jun 272011 Jun 30

Publication series

NameIEEE International Conference on Fuzzy Systems
ISSN (Print)1098-7584

Conference

Conference2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011
CountryTaiwan, Province of China
CityTaipei
Period11/6/2711/6/30

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Keywords

  • Clustering
  • Conditionally positive definite kernel
  • Fuzzy c-means

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

Cite this

Kanzawa, Y., Endo, Y., & Miyamoto, S. (2011). On hard and fuzzy c-means clustering with conditionally positive definite kernel. In FUZZ 2011 - 2011 IEEE International Conference on Fuzzy Systems - Proceedings (pp. 816-820). [6007431] (IEEE International Conference on Fuzzy Systems). https://doi.org/10.1109/FUZZY.2011.6007431