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Approximation of Optimal Two-Dimensional Association Rules for Categorical Attributes Using Semidefinite Programming

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Discovery Science (DS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1721))

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Abstract

We consider the problem of finding two-dimensional association rules for categorical attributes. Suppose we have two conditional attributes A and B both of whose domains are categorical, and one binary target attribute whose domain is “positive”, “negative”. We want to split the Cartesian product of domains of A and B into two subsets so that a certain objective function is optimized, i.e., we want to find a good segmentation of the domains of A and B. We consider in this paper the objective function that maximizes the confidence under the constraint of the upper bound of the support size. We first prove that the problem is NP-hard, and then propose an approximation algorithm based on semidefinite programming. In order to evaluate the effectiveness and efficiency of the proposed algorithm, we carry out computational experiments for problem instances generated by real sales data consisting of attributes whose domain size is a few hundreds at maximum. Approximation ratios of the solutions obtained measured by comparing solutions for semidefinite programming relaxation range from 76% to 95%. It is observed that the performance of generated association rules are significantly superior to that of one-dimensional rules.

Research of this paper is partly supported by the Grant-in-Aid for Scientific Research on Priority Areas (A) by the Ministry of Education, Science, Sports and Culture of Japan.

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Authors and Affiliations

  1. Department of Architecture and Architectural Systems, Kyoto University, Kyoto, Japan

    Katsuki Fujisawa & Naoki Katoh

  2. Department of Business Administration, Osaka Industrial University, Daito, Osaka, Japan

    Yukinobu Hamuro & Katsutoshi Yada

  3. Tokyo Research Laboratory, IBM Japan, Yamato, Japan

    Takeshi Tokuyama

Authors
  1. Katsuki Fujisawa
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  2. Yukinobu Hamuro
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  3. Naoki Katoh
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  4. Takeshi Tokuyama
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  5. Katsutoshi Yada
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Editor information

Editors and Affiliations

  1. Department of Informatics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Setsuo Arikawa

  2. Graduate School of Media and Governance, Keio University, 5322 Endoh, Fujisawa-shi, Kanagawa, 252-8520, Japan

    Koichi Furukawa

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© 1999 Springer-Verlag Berlin Heidelberg

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Fujisawa, K., Hamuro, Y., Katoh, N., Tokuyama, T., Yada, K. (1999). Approximation of Optimal Two-Dimensional Association Rules for Categorical Attributes Using Semidefinite Programming. In: Arikawa, S., Furukawa, K. (eds) Discovery Science. DS 1999. Lecture Notes in Computer Science(), vol 1721. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46846-3_14

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  • DOI: https://doi.org/10.1007/3-540-46846-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66713-1

  • Online ISBN: 978-3-540-46846-2

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