Model-based clustering assumes that the data were generated from a convex combination of densities. The choice of the density function is crucial; the multivariate contaminated normal distribution (MCN) was proposed to model datasets characterized by the presence of outliers.
The MCN is a two-component Gaussian mixture; one of the components, with a large prior probability, represents the good observations, and the other, with a small prior probability, the same mean, and an inflated covariance matrix, represents the outliers. Mixtures of MCN distributions can detect outliers and perform cluster analysis improving the clustering performance when compared to normal mixtures and representing an alternative to t mixtures.
However, the mixture of MCN distributions has two drawbacks; it assumes symmetry around the means and it uses univariate parameters to model the proportion of outliers and their impact on the inflation parameter, i.e., they are the same for all the variables. This is a limit because clusters can be skewed and the outliers may be different in each dimension.
In this talk, we will address those issues presenting a paradigm for parameterizing contamination and skewness within variants of the mixtures of shifted asymmetric Laplace (SAL) distributions. These models will be able to provide both group labels for like observations and detect whether an observation is an outlying point, unifying the fields of model-based learning and outlier detection.
Of particular interest are the multiple scaled variants of the mixtures of SAL distributions which allow for directional contamination and skewness, resulting in contours that do not have the traditional elliptical shapes.
Speaker
Professor Cristina Tortora is an Assistant Professor in the Department of Mathematics and Statistics, San Jose State University.
