Modelling Background Noise in Finite Mixtures of Generalized Linear Regression Models

In this paper we show how only a few outliers can completely break down EM-estimation of mixtures of regression models. A simple, yet very effective way of dealing with this problem, is to use a component where all regression parameters are fixed to zero to model the background noise. This noise component can be easily defined for different types of generalized linear models, has a familiar interpretation as the empty regression model, and is not very sensitive with respect to its own parameters

Выбор оптимального порядка соседства для разделения пространственного точечного образа на кластерную и шумовую составляющую (на примере анализа размещения античных поселений на Керченском полуострове)

При выполнении анализа точечного образа методом NNCR необходимо выбирать порядок соседства, который обеспечит оптимальный уровень генерализации результата, не допуская ни чрезмерной детализации, ни чрезмерного огрубления. В качестве критериев оптимального уровня соседства можно использовать вероятность наличия кластерной составляющей в точечном образе, медианное значение и межквартильный размах вероятности принадлежности для кластерной составляюще

Noise-augmented directional clustering of genetic association data identifies distinct mechanisms underlying obesity.

Funder: NIHR Cambridge Biomedical Research CentreClustering genetic variants based on their associations with different traits can provide insight into their underlying biological mechanisms. Existing clustering approaches typically group variants based on the similarity of their association estimates for various traits. We present a new procedure for clustering variants based on their proportional associations with different traits, which is more reflective of the underlying mechanisms to which they relate. The method is based on a mixture model approach for directional clustering and includes a noise cluster that provides robustness to outliers. The procedure performs well across a range of simulation scenarios. In an applied setting, clustering genetic variants associated with body mass index generates groups reflective of distinct biological pathways. Mendelian randomization analyses support that the clusters vary in their effect on coronary heart disease, including one cluster that represents elevated body mass index with a favourable metabolic profile and reduced coronary heart disease risk. Analysis of the biological pathways underlying this cluster identifies inflammation as potentially explaining differences in the effects of increased body mass index on coronary heart disease

Robustness and Outliers

Producción CientíficaUnexpected deviations from assumed models as well as the presence of certain amounts of outlying data are common in most practical statistical applications. This fact could lead to undesirable solutions when applying non-robust statistical techniques. This is often the case in cluster analysis, too. The search for homogeneous groups with large heterogeneity between them can be spoiled due to the lack of robustness of standard clustering methods. For instance, the presence of (even few) outlying observations may result in heterogeneous clusters artificially joined together or in the detection of spurious clusters merely made up of outlying observations. In this chapter we will analyze the effects of different kinds of outlying data in cluster analysis and explore several alternative methodologies designed to avoid or minimize their undesirable effects.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13

A simulations study to compare robust clustering methods based on mixtures

Abstract The following mixture model-based clustering methods are compared in a simulation study with one-dimensional data, fixed number of clusters and a focus on outliers and uniform "noise": an ML-estimator (MLE) for Gaussian mixtures, an MLE for a mixture of Gaussians and a uniform distribution (interpreted as "noise component" to catch outliers), an MLE for a mixture of Gaussian distributions where a uniform distribution over the range of the data is fixed (Fraley and Raftery in Comput J 41:578-588, 199

The Noise Component in Model-based Cluster Analysis

The so-called noise-component has been introduced by Banfield and Raftery (1993) to improve the robustness of cluster analysis based on the normal mixture model. The idea is to add a uniform distribution over the convex hull of the data as an additional mixture component. While this yields good results in many practical applications, there are some problems with the original proposal: 1) As shown by Hennig (2004), the method is not breakdown-robust. 2) The original approach doesn’t define a proper ML estimator, and doesn’t have satisfactory asymptotic properties. We discuss two alternatives. The first one consists of replacing the uniform distribution by a fixed constant, modelling an improper uniform distribution that doesn’t depend on the data. This can be proven to be more robust, though the choice of the involved tuning constant is tricky. The second alternative is to approximate the ML-estimator of a mixture of normals with a uniform distribution more precisely than it is done by the “convex hull” approach. The approaches are compared by simulations and for a real data example