High breakdown mixture discriminant analysis

Abstract

Robust S-estimation is proposed for multivariate Gaussian mixture models generalizing the work of Hastie and Tibshirani (J. Roy. Statist. Soc. Ser. B 58 (1996) 155). In the case of Gaussian Mixture models, the unknown location and scale parameters are estimated by the EM algorithm. In the presence of outliers, the maximum likelihood estimators of the unknown parameters are affected, resulting in the misclassification of the observations. The robust Sestimators of the unknown parameters replace the non-robust estimators from M-step of the EM algorithm. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using robust S-estimators as compared to the standard maximum likelihood estimators. r

Robust supervised classification with mixture models: Learning from data with uncertain labels

“…Bashir et al [2] focused on robust estimation of the model parameters in the mixture model context. Maximum likelihood estimators of the mixture model parameters are replaced by the corresponding S-estimators (see Rousseeuw and Leroy [25] for a general account on robust estimation) but the authors only observed a slight reduction of the average probability of misclassification.…”

On Locally Linear Classification by Pairwise Coupling

“…Hastie et al presented a method named mixture discriminative analysis (MDA), which uses a supervised EM algorithm to identify subclasses and a linear discriminant analysis (LDA) model to build the classifier by regarding each subclass as a pseudo-class [1]. Later, several improvements were proposed to alleviate the constraints of the LDA model [13,14]. Zhu et al presented several criterions to estimate the optimal number of subclasses (Gaussians) [5].…”

Robust Model-Based Learning via Spatial-EM Algorithm

“…Applications in a wide range of fields have emerged in the past decades. They are used for density estimation in unsupervised clustering [9], [13], [15], [25], [28], [50], for estimating class-conditional densities in supervised learning settings [1], [15], [36], and for outlier detection purposes [30], [38], [54]. Comprehensive surveys on mixture models and their applications can be found in the monographs by Titterington et al [46] and McLachlan and Peel [29].…”

“…Hardin and Rocke [17] used minimum covariance determinant (MCD) estimator for cluster analysis. Bashir and Carter [1] recommended the use of S estimator. In this paper, we propose to apply spatial rank based location and scatter estimators.…”