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On Fuzzy Clustering for Categorical Multivariate Data Induced by Polya Mixture Models

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Modeling Decisions for Artificial Intelligence (MDAI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10571))

Abstract

In this paper, three fuzzy clustering models for categorical multivariate data are proposed based on the Polya mixture model and q-divergence. A conventional fuzzy clustering model for categorical multivariate data is constructed by fuzzifying a multinomial mixture model (MMM) via regularizing Kullback-Leibler (KL) divergence appearing in a pseudo likelihood of an MMM, whereas MMM is extended to a Polya mixture model (PMM) and no fuzzy counterpart to PMM is proposed. The first proposed model is constructed by fuzzifying PMM, by means of regularizing KL-divergence appearing in a pseudo likelihood of the model. The other two models are derived by modifying the first proposed algorithm, which is based on the fact that one of the three fuzzy clustering models for vectorial data is similar to the first proposed model, and that another fuzzy clustering model for vectorial data can connect the other two fuzzy clustering models for vectorial data based on q-divergence. In numerical experiments, the properties of the membership of the proposed methods were observed using an artificial dataset.

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Acknowledgment

This work was supported by JSPS KAKENHI Grant Number 15K00348.

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Authors and Affiliations

  1. Shibaura Institute of Technology, Koto, Tokyo, 135-8548, Japan

    Yuchi Kanzawa

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  1. Yuchi Kanzawa
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Correspondence to Yuchi Kanzawa .

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Editors and Affiliations

  1. University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Toho Gakuen, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Kyushu Institute of Technology, Iizuka, Fukuoka, Japan

    Aoi Honda

  4. Kyushu Institute of Technology, Kitakyushu-shi, Fukuoka, Japan

    Sozo Inoue

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Kanzawa, Y. (2017). On Fuzzy Clustering for Categorical Multivariate Data Induced by Polya Mixture Models. In: Torra, V., Narukawa, Y., Honda, A., Inoue, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2017. Lecture Notes in Computer Science(), vol 10571. Springer, Cham. https://doi.org/10.1007/978-3-319-67422-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-67422-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67421-6

  • Online ISBN: 978-3-319-67422-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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