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Exponent and Logarithm Component-Wise Construction Method of FCM Clustering Validity Function Based on Subjective and Objective Weighting

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Abstract

The cluster validity function is used to evaluate the quality of the cluster results, and giving the exact number of initial cluster categories will rationalize the cluster results. Most single cluster validity functions and combined cluster validity functions generally have strong subjective problems, which also increases the burden on decision analysts and have great limitations in applications. To overcome the shortcomings of these clustering validity functions and improve the accuracy of the optimal cluster category classification for the datasets, based on the clustering performance evaluation components, a validity functional component construction method based on the exponential and log form was proposed. The weighting method adopts the combination of expert empowerment and standard separation method to combine the five weights so as to obtain 52 different fuzzy clustering validity functions. Then, based on the fuzzy C-mean (FCM) clustering algorithm, the performance analysis are carried out by using multiple data sets. Experimental simulation of these functions are proceeded on six commonly used UCI datasets. A clustering validity function with the simplest structure and the best classification effect was selected by comparison. Finally, this function is compared with 8 typical single clustering validity functions and four common clustering validity combination evaluation methods on 8 UCI data sets. Through experimental simulation, the proposed validity function is compared in processing data sets, but also has strong scientific theoretical basis. Thus, the feasibility and effectiveness of the proposed clustering validity function construction method are proved.

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Acknowledgements

This work was supported by the Basic Scientific Research Project of Institution of Higher Learning of Liaoning Province (Grant No. LJKZ0293), and the Project by Liaoning Provincial Natural Science Foundation of China (Grant No. 20180550700).

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Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Science & Technology Liaoning, Anshan, 114051, China

    Jia-Xu Liu, Jie-Sheng Wang, Guan Wang, Xiao-Rui Zhao & Hong-Yu Wang

  2. Inspection and Certification Center Liaoning, Anshan, 114051, China

    Di Jin

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  1. Jia-Xu Liu
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  2. Jie-Sheng Wang
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  3. Guan Wang
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  4. Xiao-Rui Zhao
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  5. Hong-Yu Wang
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  6. Di Jin
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Contributions

JL participated in the data collection, analysis, algorithm simulation, and draft writing. JW participated in the concept, design, interpretation, and commented on the manuscript. GW, XZ, HW, and DJ participated in the critical revision of this paper.

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Correspondence to Jie-Sheng Wang.

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Liu, JX., Wang, JS., Wang, G. et al. Exponent and Logarithm Component-Wise Construction Method of FCM Clustering Validity Function Based on Subjective and Objective Weighting. Int. J. Fuzzy Syst. 25, 647–669 (2023). https://doi.org/10.1007/s40815-022-01394-w

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