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The utility of clusters and a Hungarian clustering algorithm

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  • Alfred Kume
  • Stephen G Walker

Abstract

Implicit in the k–means algorithm is a way to assign a value, or utility, to a cluster of points. It works by taking the centroid of the points and the value of the cluster is the sum of distances from the centroid to each point in the cluster. The aim in this paper is to introduce an alternative way to assign a value to a cluster. Motivation is provided. Moreover, whereas the k–means algorithm does not have a natural way to determine k if it is unknown, we can use our method of evaluating a cluster to find good clusters in a sequential manner. The idea uses optimizations over permutations and clusters are set by the cyclic groups; generated by the Hungarian algorithm.

Suggested Citation

  • Alfred Kume & Stephen G Walker, 2021. "The utility of clusters and a Hungarian clustering algorithm," PLOS ONE, Public Library of Science, vol. 16(8), pages 1-23, August.
    • Handle: RePEc:plo:pone00:0255174
    DOI: 10.1371/journal.pone.0255174
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    References listed on IDEAS

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    1. Mayra Z Rodriguez & Cesar H Comin & Dalcimar Casanova & Odemir M Bruno & Diego R Amancio & Luciano da F Costa & Francisco A Rodrigues, 2019. "Clustering algorithms: A comparative approach," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-34, January.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. Patrick K. Kimes & Yufeng Liu & David Neil Hayes & James Stephen Marron, 2017. "Statistical significance for hierarchical clustering," Biometrics, The International Biometric Society, vol. 73(3), pages 811-821, September.
    4. Robert Thorndike, 1953. "Who belongs in the family?," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 267-276, December.
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