A Median-Based Consensus Rule for Distance Exponent Selection in the Framework of Intelligent and Weighted Minkowski Clustering

  • Renato Cordeiro de Amorim
  • Nadia Tahiri
  • Boris Mirkin
  • Vladimir MakarenkovEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The intelligent Minkowski and weighted Minkowski K-means are recently developed effective clustering algorithms capable of computing feature weights. Their cluster-specific weights follow the intuitive idea that a feature with a low dispersion in a specific cluster should have a greater weight in this cluster than a feature with a high dispersion. The final clustering provided by these techniques obviously depends on the selection of the Minkowski exponent. The median-based central consensus rule we introduce in this paper allows one to select an optimal value of the Minkowski exponent. Our rule takes into account the values of the Adjusted Rand Index (ARI) between clustering solutions obtained for different Minkowski exponents and selects the clustering that provides the highest average value of ARI. Our simulations, carried out with real and synthetic data, show that the proposed median-based consensus procedure usually outperforms clustering strategies based on the selection of the highest value of the Silhouette or Calinski–Harabasz cluster validity indices.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Renato Cordeiro de Amorim
    • 1
  • Nadia Tahiri
    • 2
  • Boris Mirkin
    • 3
    • 4
  • Vladimir Makarenkov
    • 2
    Email author
  1. 1.School of Computer ScienceUniversity of HertfordshireHatfieldUK
  2. 2.Département d’informatiqueUniversité du Québec à MontréalMontrealCanada
  3. 3.Department of Data Analysis and Machine IntelligenceNational Research University, Higher School of EconomicsMoscowRussia
  4. 4.Department of Computer Science and Information SystemsBirkbeck University of LondonLondonUK

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