Alfonso Gordaliza

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We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion α of contaminating data to guarantee the robustness of the method. As a characteristic feature, restrictions on the ratio between the maximum and the minimum eigenvalues of the groups(More)
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(More)
The presence of clusters in a data set is sometimes due to the existence of certain relations among the measured variables which vary depending on some hidden factors. In these cases, observations could be grouped in a natural way around linear and nonlinear structures and, thus, the problem of doing robust clustering around linear affine subspaces has(More)
The maximum likelihood estimation in the finite mixture of distributions setting is an ill-posed problem that is treatable, in practice, through the EM algorithm. However, the existence of spurious solutions (singularities and non-interesting local maximizers) makes difficult to find sensible mixture fits for non-expert practitioners. In this work, a(More)
The high prevalence of spurious solutions and the disturbing effect of outlying observations in mixture modeling are well known problems that pose serious difficulties for non-expert practitioners of this kind of models in different applied areas. An approach which combines the use of Trimmed Maximum Likelihood ideas and the imposition of restrictions on(More)
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the cluster weighted model and of an estimator based on trimming and restrictions. The selected model provides the conditional distribution of the response for each group, as in mixtures of regression, and further supplies local(More)
A new method for performing robust clustering is proposed. The method is designed with the aim of fitting clusters with different scatters and weights. A proportion α of contaminating data points is also allowed. Restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. These restrictions make(More)
Consistency and weak limit law for trimmed best k-nets are obtained in a quite general framework that covers the multivariate setting and general k 1: Consitency holds for absolutely continuous distributions without conditions on the moments and without the (arti cial) requirement of a trimming level varying with the sample size as in Cuesta-Albertos,(More)