The influence function of the TCLUST robust clustering procedure

Ruwet, Christel; García-Escudero, Luis Angel; Gordaliza, Alfonso; Mayo-Iscar, Agustin

doi:10.1007/s11634-012-0107-1

Request a copy

Article (Scientific journals)

The influence function of the TCLUST robust clustering procedure

Ruwet, Christel; García-Escudero, Luis Angel; Gordaliza, Alfonso et al.

2012 • In Advances in Data Analysis and Classification, 6 (2), p. 107-130

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/92958

DOI
10.1007/s11634-012-0107-1

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

The_IF_of_the_tclust_procedure_TR.pdf

Author postprint (357.64 kB)

Request a copy

The original publication is available at www.springerlink.com

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Heterogeneous Clustering; Influence function; Robustness; Trimmin

Abstract :

[en] The TCLUST procedure performs robust clustering with the aim of finding clusters with different scatter structures and proportions. An Eigenvalue Ratio constraint is considered by TCLUST in order to avoid finding spurious clusters. In order to guarantee the robustness of the method against the presence of outliers and background noise, the method allows for trimming of a given proportion of observations self determined by the data. This article studies robustness properties of the TCLUST procedure by means of the influence function, obtaining a robustness behavior close to that of the trimmed k-means.

Disciplines :

Mathematics

Author, co-author :

Ruwet, Christel ; Université de Liège - ULiège > Département de mathématique > Statistique mathématique

García-Escudero, Luis Angel; Universidad deValladolid - UVa

Gordaliza, Alfonso; Universidad deValladolid - UVa

Mayo-Iscar, Agustin; Universidad deValladolid - UVa

Language :

English

Title :

The influence function of the TCLUST robust clustering procedure

Publication date :

2012

Journal title :

Advances in Data Analysis and Classification

ISSN :

1862-5347

eISSN :

1862-5355

Publisher :

Springer, Germany

Volume :

Issue :

Pages :

107-130

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

Spanish Ministerio de Ciencia e Innovación
FWB - Fédération Wallonie-Bruxelles

Available on ORBi :

since 15 June 2011

Statistics

Number of views

95 (8 by ULiège)

Number of downloads

9 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Croux C, Filzmoser P, Joossens K (2008) Classification efficiencies for robust linear discriminant analysis. Stat Sin 18(2): 581-599.
Cuesta-Albertos JA, Gordaliza A, Matrán C (1997) Trimmed k-means: an attempt to robustify quantizers. Ann Stat 25(2): 553-576.
Fraley C, Raftery AE (2002) Model-based clustering, discriminant analysis, and density estimation. J Am Stat Assoc 97(458): 611-631.
Gallegos MT (2001) Robust clustering under general normal assumptions. Technical Report MIP-0103, Fakultät für Mathematik und Informatik, Universität Passau.
Gallegos MT (2002) Maximum likelihood clustering with outliers. In: Classification, clustering, and data analysis (Cracow, 2002). Studies in classification, data analysis, and knowledge organization. Springer, Berlin, pp 247-255.
Gallegos MT, Ritter G (2005) A robust method for cluster analysis. Ann Stat 33(1): 347-380.
Gallegos MT, Ritter G (2009) Trimming algorithms for clustering contaminated grouped data and their robustness. Adv Data Anal Classif 3(2): 135-167.
García-Escudero LA, Gordaliza A (1999) Robustness properties of k means and trimmed k means. J Am Stat Assoc 94(447): 956-969.
García-Escudero LA, Gordaliza A (2007) The importance of the scales in heterogeneous robust clustering. Comput Stat Data Anal 51(9): 4403-4412.
García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2008) A general trimming approach to robust cluster analysis. Ann Stat 36(3): 1324-1345.
García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2010) A review of robust clustering methods. Adv Data Anal Classif 4: 89-109.
García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2011) Exploring the number of groups in robust model-based clustering. Stat Comput 21: 585-599.
Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics. The approach based on influence functions. Wiley series in probability and mathematical statistics: probability and mathematical statistics. Wiley, New York.
Hathaway RJ (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13(2): 795-800.
Luenberger DG, Ye Y (2008) Linear and nonlinear programming. In: International series in operations research and management science, vol 116, 3rd edn. Springer, New York.
McLachlan G, Peel D (2000) Finite mixture models. Wiley series in probability and statistics: applied probability and statistics. Wiley-Interscience, New York.
Pison G, van Aelst S (2004) Diagnostic plots for robust multivariate methods. J Comput Graph Stat 13(2): 310-329.
Rousseeuw P, van Zomeren B (1990) Unmasking multivariate outliers and leverage points. J Am Stat Assoc 85: 633-651.
Ruwet C, Haesbroeck G (2011) Impact of contamination on training and test error rates in statistical clustering analysis. Commun Stat Simul Comput 40: 394-411.
Zhong S, Ghosh J (2004) A unified framework for model-based clustering. J Mach Learn Res 4(6): 1001-1037.