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See detailOn the breakdown behavior of TCLUST clustering procedure
Ruwet, Christel ULg; Garcia-Escudero, Luis Angel; Gordaliza, Alfonso et al

in Test (2013), 22(3), 466-487

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 ... [more ▼]

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 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 of contamination equal to the trimming rate as soon as the data set is sufficiently "well clustered". [less ▲]

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See detailThe influence function of the TCLUST robust clustering procedure
Ruwet, Christel ULg; García-Escudero, Luis Angel; Gordaliza, Alfonso et al

in Advances in Data Analysis and Classification [=ADAC] (2012), 6(2), 107-130

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 ... [more ▼]

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. [less ▲]

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See detailImpact of contamination on the TCLUST procedure
Ruwet, Christel ULg; García-Escudero, Luis Angel; Gordaliza, Alfonso et al

Conference (2011, December 18)

The TCLUST procedure is a robust clustering procedure that performs clus- tering with the aim of tting clusters with di erent scatters and weights. As the corresponding objective function can be unbounded ... [more ▼]

The TCLUST procedure is a robust clustering procedure that performs clus- tering with the aim of tting clusters with di erent scatters and weights. As the corresponding objective function can be unbounded, a restriction is added on the eigenvalues-ratio of the scatter matrices. The robustness of the method is guaranteed by allowing the trimming of a given proportion of observations. The resistance to contamination of that procedure will be studied. Results con- cerning breakdown points and some new criteria in robust cluster analysis, such as the dissolution point and the isolation robustness, will be presented. [less ▲]

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See detailRobustness properties of the TCLUST procedure
Ruwet, Christel ULg; García-Escudero, Luis Angel; Gordaliza, Alfonso et al

Conference (2011, July 27)

The TCLUST procedure is a robust clustering procedure introduced by García-Escudero et al. (2008). It performs clustering with the aim of fitting clusters with different scatters and weights. As the ... [more ▼]

The TCLUST procedure is a robust clustering procedure introduced by García-Escudero et al. (2008). It performs clustering with the aim of fitting clusters with different scatters and weights. As the corresponding objective function can be unbounded, a restriction is added on the eigenvalues-ratio of the scatter matrices. The robustness of the method is guaranteed by allowing the trimming of a given proportion of observations. As García-Escudero and Gordaliza (1999) have done for the k-means and trimmed k-means methodologies, the robustness properties of the TCLUST procedure are studied by means of the influence function and the breakdown point. In order to be able to compare the robustness of TCLUST with other clustering methods, dissolution point and isolation robustness (Hennig, 2008) are also considered. It turns out that the TCLUST procedure has a behavior close to that of the trimmed k-means. [less ▲]

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See detailThe breakdown bahavior of the TCLUST procedure
Ruwet, Christel ULg; García-Escudero, Luis Angel; Gordaliza, Alfonso et al

Conference (2011, May 18)

The TCLUST procedure is a new robust clustering method introduced by García-Escudero et al. (2008). It performs clustering with the aim of finding clusters with different scatters and weights. As the ... [more ▼]

The TCLUST procedure is a new robust clustering method introduced by García-Escudero et al. (2008). It performs clustering with the aim of finding clusters with different scatters and weights. As the corresponding objective function can be unbounded, a restriction is added on the eigenvalues-ratio of the scatter matrices. The robustness of the method is guaranteed by allowing the trimming of a given proportion of observations. This trimming level has to be chosen by the practitioner, as well as the number of clusters. Suitable values for these parameters can be obtained throughout the careful examination of some classification trimmed likelihood curves (García-Escudero et al., 2010). The first part of this talk will consist of a brief presentation of this clustering procedure and the related R package (tclust). In the second part of the talk, the robustness of the TCLUST procedure, and more precisely its breakdown behavior, will be studied. In the context of cluster analysis, Hennig (2004, 2008) has defined some useful concepts to characterize the breakdown of a procedure; the r-components breakdown point, the dissolution point and the isolation robustness. These tools will be applied to the TCLUST procedure and some examples will be presented. [less ▲]

Detailed reference viewed: 23 (4 ULg)