Mixture Model-Based Classification

"This is a great overview of the field of model-based clustering and classification by one of its leading developers. McNicholas provides a resource that I am certain will be used by researchers in statistics and related disciplines for quite some time. The discussion of mixtures with heavy tails and asymmetric distributions will place this text as the authoritative, modern reference in the mixture modeling literature." (Douglas Steinley, University of Missouri) Mixture Model-Based Classification is the first monograph devoted to mixture model-based approaches to clustering and classification. This is both a book for established researchers and newcomers to the field. A history of mixture models as a tool for classification is provided and Gaussian mixtures are considered extensively, including mixtures of factor analyzers and other approaches for high-dimensional data. Non-Gaussian mixtures are considered, from mixtures with components that parameterize skewness and/or concentration, right up to mixtures of multiple scaled distributions. Several other important topics are considered, including mixture approaches for clustering and classification of longitudinal data as well as discussion about how to define a cluster Paul D. McNicholas is the Canada Research Chair in Computational Statistics at McMaster University, where he is a Professor in the Department of Mathematics and Statistics. His research focuses on the use of mixture model-based approaches for classification, with particular attention to clustering applications, and he has published extensively within the field. He is an associate editor for several journals and has served as a guest editor for a number of special issues on mixture models.

Introduction Classification Finite Mixture Models Model-Based Clustering, Classification and Discriminant AnalysisComparing Partitions Packages Data Sets Outline of the Contents of this Monograph Mixtures of Multivariate Gaussian Distributions Historical Development Parameter Estimation Gaussian Parsimonious Clustering Models Model Selection Merging Gaussian Components Illustrations Comments Mixtures of Factor Analyzers And Extensions Factor Analysis Mixture of Factor Analyzers Parsimonious Gaussian Mixture Models Expanded Parsimonious Gaussian Mixture Models Mixture of Common Factor Analyzers Illustrations Comments Dimension Reduction and High-Dimensional Data Implicit and Explicit Approaches The PGMM Family in High-Dimensional Applications VSCC clustvarsel and selvarclust GMMDR HD-GMM Illustrations Comments Mixtures of Distributions with Varying Tail Weight Mixtures of Multivariate t-Distributions Mixtures of Power Exponential Distributions Illustrations Comments Mixtures of Generalized Hyperbolic Distributions Overview Generalized Inverse Gaussian Distribution Mixtures of Shifted Asymmetrical Laplace Distributions SAL Mixtures Versus Gaussian Mixtures Mixture of Generalized Hyperbolic Distributions Mixture of Generalized Hyperbolic Factor Analyzers Illustrations Note on Normal Variance-Mean MixturesComments Mixtures of Multiple Scaled Distributions Overview Mixture of Multiple Scaled t-Distributions Mixture of Multiple Scaled SAL Distributions Mixture of Multiple Scaled Generalized Hyperbolic DistributionsMixture of Coalesced Generalized Hyperbolic Distributions Cluster Convexity Illustrations Comments Methods for Longitudinal Data Modified Cholesky Decomposition Gaussian Mixture Modelling of Longitudinal Data Using t-Mixtures Illustrations Comments Miscellania On the Definition of a Cluster What is the Best Way to Perform Clustering, Classification, and Discriminant Analysis?Mixture Model Averaging Robust Clustering Clustering Categorical Data Cluster-Weighted Models Mixed-Type Data Alternatives to the EM Algorithm Challenges and Open Questions A Useful Mathematical Results Bibliography

Paul D. McNicholas is the Canada Research Chair in Computational Statistics at McMaster University, where he is a Professor in the Department of Mathematics and Statistics. His research focuses on the use of mixture model-based approaches for classification, with particular attention to clustering applications, and he has published extensively within the field. He is an associate editor for several journals and has served as a guest editor for a number of special issues on mixture models.