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On Strategies to Fix Degenerate k-means Solutions

Author

Listed:
  • Daniel Aloise

    (Polytechnique Montréal
    Polytechnique Montréal)

  • Nielsen Castelo Damasceno

    (Federal University of Rio Grande do Norte)

  • Nenad Mladenović

    (LAMIH, Université de Valenciennes et du Hainaut Cambrésis)

  • Daniel Nobre Pinheiro

    (Federal University of Rio Grande do Norte)

Abstract

k-means is a benchmark algorithm used in cluster analysis. It belongs to the large category of heuristics based on location-allocation steps that alternately locate cluster centers and allocate data points to them until no further improvement is possible. Such heuristics are known to suffer from a phenomenon called degeneracy in which some of the clusters are empty. In this paper, we compare and propose a series of strategies to circumvent degenerate solutions during a k-means execution. Our computational experiments show that these strategies are effective, leading to better clustering solutions in the vast majority of the cases in which degeneracy appears in k-means. Moreover, we compare the use of our fixing strategies within k-means against the use of two initialization methods found in the literature. These results demonstrate how useful the proposed strategies can be, specially inside memorybased clustering algorithms.

Suggested Citation

  • Daniel Aloise & Nielsen Castelo Damasceno & Nenad Mladenović & Daniel Nobre Pinheiro, 2017. "On Strategies to Fix Degenerate k-means Solutions," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 165-190, July.
    • Handle: RePEc:spr:jclass:v:34:y:2017:i:2:d:10.1007_s00357-017-9231-0
    DOI: 10.1007/s00357-017-9231-0
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    References listed on IDEAS

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    1. Pierre Hansen & Eric Ngai & Bernard K. Cheung & Nenad Mladenovic, 2005. "Analysis of Global k-Means, an Incremental Heuristic for Minimum Sum-of-Squares Clustering," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 287-310, September.
    2. Joeri Hofmans & Eva Ceulemans & Douglas Steinley & Iven Mechelen, 2015. "On the Added Value of Bootstrap Analysis for K-Means Clustering," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 268-284, July.
    3. Emilio Carrizosa & Abdulrahman Alguwaizani & Pierre Hansen & Nenad Mladenović, 2015. "New heuristic for harmonic means clustering," Journal of Global Optimization, Springer, vol. 63(3), pages 427-443, November.
    4. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    5. Simon Blanchard & Daniel Aloise & Wayne DeSarbo, 2012. "The Heterogeneous P-Median Problem for Categorization Based Clustering," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 741-762, October.
    6. Michael Brusco & Douglas Steinley, 2007. "A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 583-600, December.
    7. Pacheco, Joaquin & Valencia, Olga, 2003. "Design of hybrids for the minimum sum-of-squares clustering problem," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 235-248, June.
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    Cited by:

    1. Aurora Torrente & Juan Romo, 2021. "Initializing k-means Clustering by Bootstrap and Data Depth," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 232-256, July.

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