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Assessing clustering methods using Shannon's entropy

Author

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  • Anis Hoayek

    (LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes - ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne - CNRS - Centre National de la Recherche Scientifique - UCA - Université Clermont Auvergne - INP Clermont Auvergne - Institut national polytechnique Clermont Auvergne - UCA - Université Clermont Auvergne, FAYOL-ENSMSE - Institut Henri Fayol - Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris], FAYOL-ENSMSE - Département Génie mathématique et industriel - ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne - Institut Henri Fayol, Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris])

  • Didier Rullière

    (LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes - ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne - CNRS - Centre National de la Recherche Scientifique - UCA - Université Clermont Auvergne - INP Clermont Auvergne - Institut national polytechnique Clermont Auvergne - UCA - Université Clermont Auvergne, FAYOL-ENSMSE - Institut Henri Fayol - Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris], FAYOL-ENSMSE - Département Génie mathématique et industriel - ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne - Institut Henri Fayol, Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris])

Abstract

Unsupervised clustering techniques are a valuable source of information for determining how to divide a dataset into subgroups. We present a comprehensive analysis of the quality of these algorithms by defining a clustering fuzziness metric. A statistical test and cluster probabilities corrections are provided based on this metric. Some examples demonstrate how it can be used to compare different clustering algorithms or improve the accuracy of various methods. An application for adjusting the number of clusters is also presented. These results are illustrated using both simulated and real-world data.

Suggested Citation

  • Anis Hoayek & Didier Rullière, 2024. "Assessing clustering methods using Shannon's entropy," Post-Print hal-03812055, HAL.
    • Handle: RePEc:hal:journl:hal-03812055
    DOI: 10.1016/j.ins.2024.121510
    Note: View the original document on HAL open archive server: https://hal.science/hal-03812055v2
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