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Fuzzy Classification Function of Standard Fuzzy c-Means Algorithm for Data with Tolerance Using Kernel Function

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Modeling Decisions for Artificial Intelligence (MDAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5285))

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Abstract

In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed.

First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

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References

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Author information

Authors and Affiliations

  1. Shibaura Institute of Technology, 3-7-5 Toyosu, Koto, Tokyo, 135-8548, Japan

    Yuchi Kanzawa

  2. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Yasunori Endo & Sadaaki Miyamoto

Authors
  1. Yuchi Kanzawa
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  2. Yasunori Endo
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  3. Sadaaki Miyamoto
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Editor information

Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council,, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen,, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

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© 2008 Springer-Verlag Berlin Heidelberg

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Kanzawa, Y., Endo, Y., Miyamoto, S. (2008). Fuzzy Classification Function of Standard Fuzzy c-Means Algorithm for Data with Tolerance Using Kernel Function. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_12

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  • DOI: https://doi.org/10.1007/978-3-540-88269-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88268-8

  • Online ISBN: 978-3-540-88269-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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