Journal of Classification

, Volume 34, Issue 2, pp 165–190 | Cite as

On Strategies to Fix Degenerate k-means Solutions

  • Daniel AloiseEmail author
  • Nielsen Castelo Damasceno
  • Nenad Mladenović
  • Daniel Nobre Pinheiro


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.


k-means Minimum sum-of-squares Degeneracy Clustering Heuristics 


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Copyright information

© Classification Society of North America 2017

Authors and Affiliations

  • Daniel Aloise
    • 1
    • 4
    Email author
  • Nielsen Castelo Damasceno
    • 2
  • Nenad Mladenović
    • 3
  • Daniel Nobre Pinheiro
    • 2
  1. 1.Polytechnique MontréalMontréalCanada
  2. 2.Federal University of Rio Grande do NorteRio GrandeBrazil
  3. 3.LAMIH, Université de Valenciennes et du Hainaut CambrésisValenciennesFrance
  4. 4.Department of Computer EngineeringPolytechnique MontréalMontréalCanada

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