Robust fitting of mixtures using the trimmed likelihood estimator

Neykov, N. M.; Filzmoser, Peter; Dimova, Rositsa B.; Neytchev, P. N.

doi:10.1016/j.csda.2006.12.024

Cited by 147 publications

(114 citation statements)

References 11 publications

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“…Though interesting, this issue is beyond the scope of the present paper. Surely, some datadependent diagnostic based on trimmed BIC notions (Neykov et al, 2007) may provide a way to select the number of groups and underlying factors, as has been shown. With reference to the choice of α, other tools can be adapted to the present case, such as silhouette plots to assess the strength of cluster assignments and the classification trimmed likelihood curves (García-Escudero et al, 2011).…”

Section: Discussionmentioning

confidence: 99%

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The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

García-Escudero

Gordaliza

Greselin

et al. 2016

Computational Statistics & Data Analysis

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Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering -at the same time -dimension reduction and model-based clustering. The high prevalence of spurious solutions and the disturbing effects of outlying observations in maximum likelihood estimation may cause biased or misleading inferences. Restrictions for the component covariances are considered in order to avoid spurious solutions, and trimming is also adopted, to provide robustness against violations of the normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.

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Section: Discussionmentioning

confidence: 99%

“…, x n } be a given data set in R p . With the theoretical underlying model described in Section 3 in mind, a mixture of Gaussian factor components can be robustly fitted to this dataset x by maximizing a trimmed mixture log-likelihood (see Neykov et al 2007, Gallegos and Ritter 2009and García-Escudero et al 2014) defined as:…”

Section: Problem Statementmentioning

confidence: 99%

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

García-Escudero

Gordaliza

Greselin

et al. 2016

Computational Statistics & Data Analysis

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“…The here presented "trimming" approach differs from "robust mixture modeling" ones in that noisy data are completely avoided and no attempt to fit them is tried. A "trimming" approach to mixture modeling can be found in Neykov et al (2004 and2007) and in Cuesta-Albertos et al (2008). Take also into account that "mixture modeling" and "crisp clustering" approaches pursue different goals and so answers to our initial questions may be completely different (see, Biernacki, Celeux and Govaert 2000).…”

Section: Introductionmentioning

confidence: 99%

“…When trimming is allowed, some recent proposals for choosing k and α are based on modified BIC notions (Neykov et al 2007and Gallegos and Ritter 2009and 2010. Gallegos and Ritter's proposals also include the consideration of normality goodnessof-fit tests and outlier identification tools (see, e.g., Becker and Gather 1999 and references therein).…”

Section: Introductionmentioning

confidence: 99%

Exploring the number of groups in robust model-based clustering

et al. 2010

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Two key questions in Clustering problems are how to determine the number of groups properly and measure the strength of group-assignments. These questions are specially involved when the presence of certain fraction of outlying data is also expected.Any answer to these two key questions should depend on the assumed probabilisticmodel, the allowed group scatters and what we understand by noise. With this in mind, some exploratory "trimming-based" tools are presented in this work together with their justifications. The monitoring of optimal values reached when solving a robust clustering criteria and the use of some "discriminant" factors are the basis for these exploratory tools.

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“…The second idea, which distinguishes the approach from other trimming-based methods (e.g. Neykov et al 2007), is to constrain the group scatters in order to make the optimization of the likelihood (which is unbounded otherwise) well-posed and to reduce the possibility of spurious solutions.…”

Section: Introductionmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

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We assess the performance of state-of-the-art robust clustering tools for regression structures under a variety of different data configurations. We focus on two methodologies that use trimming and restrictions on group scatters as their main ingredients. We also give particular care to the data generation process through the development of a flexible simulation tool for mixtures of regressions, where the user can control the degree of overlap between the groups. Level of trimming and restriction factors are input parameters for which appropriate tuning is required. Since we find that incorrect specification of the second-level trimming in the Trimmed CLUSTering REGression model (TCLUST-REG) can deteriorate the performance of the method, we propose an improvement where the second-level trimming is not fixed in advance but is data dependent. We then compare our adaptive version of TCLUST-REG with the Trimmed Cluster Weighted Restricted Model (TCWRM) which provides a powerful extension of the robust clusterwise regression methodology. Our overall conclusion is that the two methods perform comparably, but with notable differences due to the inherent degree of modeling implied by them.

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Robust fitting of mixtures using the trimmed likelihood estimator

Cited by 147 publications

References 11 publications

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

Exploring the number of groups in robust model-based clustering

Assessing trimming methodologies for clustering linear regression data

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