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A dissimilarity measure for mixed nominal and ordinal attribute data in k-Modes algorithm

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Abstract

Among the existing clustering algorithms, the k-Means algorithm is one of the most commonly used clustering methods. As an extension of the k-Means algorithm, the k-Modes algorithm has been widely applied to categorical data clustering by replacing means with modes. However, there are more mixed-type data containing categorical, ordinal and numerical attributes. Mixed-type data clustering problem has recently attracted much attention from the data mining research community, but most of them fail to notice the ordinal attributes and establish explicit metric similarity of ordinal attributes. In this paper, the limitations of some existing dissimilarity measure of k-Modes algorithm in mixed ordinal and nominal data are analyzed by using some illustrative examples. Based on the idea of mining ordinal information of ordinal attribute, a new dissimilarity measure for the k-Modes algorithm to cluster this type of data is proposed. The distinct characteristic of the new dissimilarity measure is to take account of the ordinal information of ordinal attribute. A convergence study and time complexity of the k-Modes algorithm based on this new dissimilarity measure indicates that it can be effectively used for large data sets. The results of comparative experiments on nine real data sets from UCI show the effectiveness of the new dissimilarity measure.

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Acknowledgments

We would also like to thank the anonymous reviewers for their helpful suggestions. This work was supported by National Natural Science Foundation of China(61573266).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Fang Yuan & Youlong Yang

  2. School of Management, Northwestern Polytechnical University, Xi’an, 710071, People’s Republic of China

    Tiantian Yuan

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  1. Fang Yuan
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  2. Youlong Yang
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  3. Tiantian Yuan
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Correspondence to Fang Yuan.

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Yuan, F., Yang, Y. & Yuan, T. A dissimilarity measure for mixed nominal and ordinal attribute data in k-Modes algorithm. Appl Intell 50, 1498–1509 (2020). https://doi.org/10.1007/s10489-019-01583-5

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