Mixture models and atypical values

Campbell, N. A.

doi:10.1007/bf01886327

Cited by 53 publications

(34 citation statements)

References 15 publications

(16 reference statements)

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“…A common way in which robust fitting of normal mixture models has been undertaken, is by using M-estimates to update the component estimates on the M-step of the EM algorithm, as in McLachlan andBasford (1988) andCampbell (1994). In this case, the updated component means are/~}k+l) are given by (9), but where now the weights u!…”

Section: Previous Work On M-estimation Of Componentsmentioning

confidence: 99%

“…The problem of providing protection against outliers in multivariate data is a very difficult problem and increases with the difficulty of the dimension of the data (Rocke and Woodruff (1997)). The related problem of making clustering algorithms more robust has received much attention recently as, for example, in McLachlan and Basford (1988, Chapter 3), De Veaux and Kreiger (1990), Campbell (1994, Dav~ and Krishnapuram (1996), Frigui and Krishnapuram (1996), Kharin (1996), and Rousseeuw, Kaufman, and Trauwaert (1996), and Zhuang et al (1996), among others. In the past, there have been many attempts at modifying existing methods of cluster analysis to provide robust clustering procedures.…”

Section: Introductionmentioning

confidence: 99%

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Robust cluster analysis via mixtures of multivariate t-distributions

McLachlan

Peel

1998

Advances in Pattern Recognition

113

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Abstract. Normal mixture models are being increasingly used as a way of clustering sets of continuous multivariate data. They provide a probabilistic (soft) clustering of the data in terms of their fitted posterior probabilities of membership of the mixture components corresponding to the clusters. An outright (hard) clustering can be subsequently obtained by assigning each observation to the component to which it has the highest fitted posterior probability of belonging. However, outliers in the data can affect the estimates of the parameters in the normal component densities, and hence the implied clustering. A more robust approach is to fit mixtures of multivariate t~distributions, which have longer tails than the normal components. The expectation-maximization (EM) algorithm can be used to fit mixtures of t-distributions by maximum likelihood. The application of this model to provide a robust approach to clustering is illustrated on a real data set. It is demonstrated how the use of t-components provides less extreme estimates of the posterior probabilities of cluster membership.

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Section: Previous Work On M-estimation Of Componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust cluster analysis via mixtures of multivariate t-distributions

McLachlan

Peel

1998

Advances in Pattern Recognition

113

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“…Within the Gaussian mixture paradigm, Campbell (1984), McLachlan and Basford (1988), Kharin (1996), and De Veaux and Krieger (1990) achieve a similar effect by using M-estimators (Huber 1964(Huber , 1981 of the means and covariance matrices of the Gaussian components of the mixture model. In a similar vein, Markatou (2000) utilizes a weighted likelihood approach to obtain robust parameter estimates.…”

Section: Robust Clusteringmentioning

confidence: 95%

Model-Based Clustering

McNicholas

2016

J Classif

185

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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“…For example, Campbell (1984) follows this approach to update the components of a Gaussian mixture in the M step of the EM algorithm. In the same spirit, Hennig (2003) uses M-estimation in clusterwise regression, in combination with an iteratively reweighted algorithm with zero weight for the outliers.…”

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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Mixture models and atypical values

Cited by 53 publications

References 15 publications

Robust cluster analysis via mixtures of multivariate t-distributions

Robust cluster analysis via mixtures of multivariate t-distributions

Model-Based Clustering

Assessing trimming methodologies for clustering linear regression data

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