On the breakdown behavior of the TCLUST clustering procedure

C. Ruwet ^[1] ; L. A. García-Escudero ^[2] ; A. Gordaliza ^[2] ; A. Mayo-Iscar ^[2]
1. [1] University of Liège
  
  University of Liège
  
  Arrondissement de Liège, Bélgica
2. [2] Universidad de Valladolid
  
  Universidad de Valladolid
  
  Valladolid, España
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 22, Nº. 3, 2013, págs. 466-487
Idioma: inglés
DOI: 10.1007/s11749-012-0312-4
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Resumen
- 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”.