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Optimization of Fuzzy C-Means with Alternating Direction Method of Multipliers

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Optimization and Learning (OLA 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1824))

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Abstract

Among the clustering methods, K-Means and its variants are very popular. These methods solve at each iteration the first-order optimality conditions. However, in some cases, the function to be minimized is not convex, as for the Fuzzy C-Means version with Mahalanobis distance (FCM-GK). In this study, we apply the Alternating Directions Method of Multiplier (ADMM) to ensure a good convergence. ADMM is often applied to solve a separable convex minimization problem with linear constraints. ADMM is a decomposition/coordination method with a coordination step provided by Lagrange multipliers. By appropriately introducing auxiliary variables, this method allows the problem to be decomposed into easily solvable convex subproblems while keeping the same iterative structure. Numerical results have demonstrated the significant performance of the proposed method compared to the standard method, especially for high-dimensional data.

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Notes

  1. 1.

    https://archive.ics.uci.edu/ml/datasets.php.

  2. 2.

    https://cs.joensuu.fi/sipu/datasets/.

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Authors and Affiliations

  1. Université Clermont Auvergne, Clermont Auvergne INP, CNRS, LIMOS, 63000, Clermont-Ferrand, France

    Benoit Albert, Violaine Antoine & Jonas Koko

Authors
  1. Benoit Albert
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  2. Violaine Antoine
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  3. Jonas Koko
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Corresponding author

Correspondence to Benoit Albert .

Editor information

Editors and Affiliations

  1. University of Cadiz, Cadiz, Spain

    Bernabé Dorronsoro

  2. University of Malaga, Malaga, Spain

    Francisco Chicano

  3. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Gregoire Danoy

  4. University of Lille, Lille, France

    El-Ghazali Talbi

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Albert, B., Antoine, V., Koko, J. (2023). Optimization of Fuzzy C-Means with Alternating Direction Method of Multipliers. In: Dorronsoro, B., Chicano, F., Danoy, G., Talbi, EG. (eds) Optimization and Learning. OLA 2023. Communications in Computer and Information Science, vol 1824. Springer, Cham. https://doi.org/10.1007/978-3-031-34020-8_21

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  • DOI: https://doi.org/10.1007/978-3-031-34020-8_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34019-2

  • Online ISBN: 978-3-031-34020-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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