The α -Groups under Condorcet Clustering

Tarik Faouzi, Luis Firinguetti-Limone, José Miguel Avilez-Bozo and Rubén Carvajal-Schiaffino
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Tarik Faouzi: Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
Luis Firinguetti-Limone: Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
José Miguel Avilez-Bozo: Departamento de Estadística, Universidad del Bío-Bío, Concepción 4051381, Chile
Rubén Carvajal-Schiaffino: Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Santiago 9170020, Chile

Mathematics, 2022, vol. 10, issue 5, 1-20

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.

Keywords: k -modes; Condorcet clustering; categorical data; quality index; within-cluster sum-of-squares index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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