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The α -Groups under Condorcet Clustering

Author

Listed:
  • Tarik Faouzi

    (Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
    These authors contributed equally to this work.)

  • Luis Firinguetti-Limone

    (Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
    These authors contributed equally to this work.)

  • José Miguel Avilez-Bozo

    (Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
    These authors contributed equally to this work.)

  • Rubén Carvajal-Schiaffino

    (Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Santiago 9170020, Chile
    These authors contributed equally to this work.)

Abstract

We introduce a new approach to clustering categorical data: Condorcet clustering with a fixed number of groups, denoted α -Condorcet. As k -modes, this approach is essentially based on similarity and dissimilarity measures. The paper is divided into three parts: first, we propose a new Condorcet criterion, with a fixed number of groups (to select cases into clusters). In the second part, we propose a heuristic algorithm to carry out the task. In the third part, we compare α -Condorcet clustering with k -modes clustering. The comparison is made with a quality’s index, accuracy of a measurement, and a within-cluster sum-of-squares index. Our findings are illustrated using real datasets: the feline dataset and the US Census 1990 dataset.

Suggested Citation

  • Tarik Faouzi & Luis Firinguetti-Limone & José Miguel Avilez-Bozo & Rubén Carvajal-Schiaffino, 2022. "The α -Groups under Condorcet Clustering," Mathematics, MDPI, vol. 10(5), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:718-:d:757595
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