Entropy Regularized Fuzzy c-Means for Data with Tolerance introducing Penalty Term in Feature Space

• Kanzawa Yuchi

  Shibaura Institute of Technology

• Endo Yasunori

  University of Tsukuba

• Miyamoto Sadaaki

  University of Tsukuba

Abstract

A new fuzzy c-means algorithms for data with tolerance is proposed by introducing a penalty term in feature space. Its idea is derived from that support vector machine introducing a penalty term for "soft margin" in feature space. In the proposed method, the data is allowed to move for minimizing the corresponding objective function but this move-ness is controlled by the penalty term. First, an optimization problem is shown by introducing tolerance with conventional fuzzy c-means algorithm in feature space. Second, Karush-Kuhn-Tucker~(KKT) conditions of the optimization problem is considered. Third, an iterative algorithm is proposed by re-expressing the KKT conditions using kernel trick. Fourth, another iterative algorithm is proposed for fuzzy classification function, which shows how prototypical an arbitrary point in the data space is to the obtained each cluster by extending the membership to the whole spa ce. Last, some numerical examples are shown.

Journal

• SCIS & ISIS

  SCIS & ISIS 2008 (0), 578-581, 2008

  Japan Society for Fuzzy Theory and Intelligent Informatics

Keywords

• Fuzzy c-means
• clustering
• kernel function

Details

• CRID: 1390001205589536256
• NII Article ID: 130004672990
• DOI: 10.14864/softscis.2008.0.578.0
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed