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On the breakdown behavior of the TCLUST clustering procedure

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  • C. Ruwet
  • L. García-Escudero
  • A. Gordaliza
  • A. Mayo-Iscar

Abstract

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”. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • C. Ruwet & L. García-Escudero & A. Gordaliza & A. Mayo-Iscar, 2013. "On the breakdown behavior of the TCLUST clustering procedure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 466-487, September.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:3:p:466-487
    DOI: 10.1007/s11749-012-0312-4
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    References listed on IDEAS

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    1. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 89-109, September.
    2. C. Ruwet & L. García-Escudero & A. Gordaliza & A. Mayo-Iscar, 2012. "The influence function of the TCLUST robust clustering procedure," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(2), pages 107-130, July.
    3. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.
    4. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
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    Cited by:

    1. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.

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    More about this item

    Keywords

    Breakdown point; Clustering; Robustness; TCLUST; Trimming; 62H30; 62F35; 62G35;
    All these keywords.

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