On the breakdown behavior of the TCLUST clustering procedure

• Published in: Test (Madrid, Spain) Vol. 22; no. 3; pp. 466 - 487
• Main Authors: Ruwet, C., García-Escudero, L. A., Gordaliza, A., Mayo-Iscar, A.
• Format: Journal Article Web Resource
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2013; Springer Nature B.V; Springer
• Subjects: Breakdown; Breakdown point; Cluster analysis; Clustering; Datasets; Economics; Eigenvalues; Euclidean space; Finance; Insurance; Management; Mathematics; Mathematics and Statistics; Mathématiques; Original Paper; Physical, chemical, mathematical & earth Sciences; Physique, chimie, mathématiques & sciences de la terre; Robustness; Statistical Theory and Methods; Statistics; Statistics for Business; Studies; TCLUST; Test methods; Trimming; United States > US; TCLUST; 62H30; Robustness; Clustering; 62F35; Breakdown point; 62G35; Trimming
• DOI: 10.1007/s11749-012-0312-4
• ISSN: 1133-0686; 1863-8260

Clustering procedures allowing for general covariance structures of the obtained clusters need some constraints on the solutions. With this in mind, several proposals have been introduced in the literature. The TCLUST procedure works with a restriction on the “eigenvalues-ratio” of the clusters scatter matrices. In order to try to achieve robustness with respect to outliers, the procedure allows to trim off a proportion α of the most outlying observations. The resistance to infinitesimal contamination of the TCLUST has already been studied. This paper aims to look at its resistance to a higher amount of contamination by means of the study of its breakdown behavior. The rather new concept of restricted breakdown point will demonstrate that the TCLUST procedure resists to a proportion α of contamination as soon as the data set is sufficiently “well clustered”.