[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 :
6
Issue :
2
Pages :
107-130
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
Spanish Ministerio de Ciencia e Innovación FWB - Fédération Wallonie-Bruxelles [BE]
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.