The <i>α</i>-Groups under Condorcet Clustering

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

• <i>k</i>-modes
• Condorcet clustering
• categorical data
• quality index
• within-cluster sum-of-squares index