Gaussian parsimonious clustering models with covariates and a noise component

• Published in: Advances in data analysis and classification Vol. 14; no. 2; pp. 293 - 325
• Main Authors: Murphy, Keefe, Murphy, Thomas Brendan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020; Springer Nature B.V
• Subjects: Algorithms; Chemistry and Earth Sciences; Clustering; Computer Science; Covariance matrix; Data Mining and Knowledge Discovery; Economics; Finance; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Multivariate analysis; Noise; Outliers (statistics); Physics; Regular Article; Software; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; Noise component; Covariates; Model-based clustering; Parsimony; Mixtures of experts; Multivariate response; EM algorithm; 62H25; 62J12
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-019-00373-8

We consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow different subsets of covariates to influence the component weights and/or component densities by modelling the parameters of the mixture as functions of the covariates. A familiar range of constrained eigen-decomposition parameterisations of the component covariance matrices are also accommodated. This paper thus addresses the equivalent aims of including covariates in Gaussian parsimonious clustering models and incorporating parsimonious covariance structures into all special cases of the Gaussian mixture of experts framework. The MoEClust models demonstrate significant improvement from both perspectives in applications to both univariate and multivariate data sets. Novel extensions to include a uniform noise component for capturing outliers and to address initialisation of the EM algorithm, model selection, and the visualisation of results are also proposed.