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Generalization Property of Fuzzy Classification Function for Tsallis Entropy-Regularization of Bezdek-Type Fuzzy C-Means Clustering

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Modeling Decisions for Artificial Intelligence (MDAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12256))

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Abstract

In this study, Tsallis entropy-regularized Bezdek-type fuzzy c-means clustering method is proposed. Because the proposed method reduces to four conventional fuzzy clustering methods by appropriately controlling fuzzification parameters, the proposed method is considered to be their generalization. Through numerical experiments, this generalization property is confirmed; in addition, it is observed that the fuzzy classification function of the proposed method approaches a value equal to the reciprocal of the cluster number.

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Authors and Affiliations

  1. Shibaura Institute of Technology, Tokyo, Japan

    Yuchi Kanzawa

Authors
  1. Yuchi Kanzawa
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Correspondence to Yuchi Kanzawa .

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Editors and Affiliations

  1. Department of Computing Science, Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Department of Management Science, Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

  3. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Jordi Nin

  4. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Núria Agell

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Kanzawa, Y. (2020). Generalization Property of Fuzzy Classification Function for Tsallis Entropy-Regularization of Bezdek-Type Fuzzy C-Means Clustering. In: Torra, V., Narukawa, Y., Nin, J., Agell, N. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2020. Lecture Notes in Computer Science(), vol 12256. Springer, Cham. https://doi.org/10.1007/978-3-030-57524-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-57524-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57523-6

  • Online ISBN: 978-3-030-57524-3

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