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A Novel Multiple Fuzzy Clustering Method Based on Internal Clustering Validation Measures with Gradient Descent

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Abstract

In this paper, we propose a novel multiple fuzzy clustering method based on internal clustering validation measures with gradient descent. Firstly, some single fuzzy clustering algorithms such as Fuzzy C-Means, Kernel Fuzzy C-Means and Gustafson–Kessel are used to construct similarity matrixes for each partition. Secondly, those similarity matrixes are aggregated into a final one by means of the direct sum of weighted vectors where the values of weights are determined by internal clustering validation measures. Finally, final membership matrix is calculated by minimizing the sum of square errors through the gradient descent method. The proposed approach has been validated in terms of clustering quality on UCI Machine Learning Repository datasets. Experimental results show that the proposed approach’s performance is better than those of other ensemble and standalone methods.

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Acknowledgments

The authors are greatly indebted to the Editor-in-chief, Prof. Shun-Feng Su, and anonymous reviewers for their comments and valuable suggestions that improved the quality and clarity of this paper. A special thanks to Mr. Pham Van Viet, HUST, for coding of algorithms in the revision stage. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.05-2014.01.

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Authors and Affiliations

  1. Division of Data Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Hoang Son

  2. Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Hoang Son

  3. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Pham Van Hai

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  1. Le Hoang Son
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  2. Pham Van Hai
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Correspondence to Pham Van Hai.

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Son, L.H., Van Hai, P. A Novel Multiple Fuzzy Clustering Method Based on Internal Clustering Validation Measures with Gradient Descent. Int. J. Fuzzy Syst. 18, 894–903 (2016). https://doi.org/10.1007/s40815-015-0117-1

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  • DOI: https://doi.org/10.1007/s40815-015-0117-1

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