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Mixture Model-Based Classification




ISBN 9781482225662
Published August 19, 2016 by Chapman and Hall/CRC
212 Pages - 38 B/W Illustrations

 
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Book Description

"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.

Table of Contents

Introduction
Classification
Finite Mixture Models
Model-Based Clustering, Classification and Discriminant Analysis
Comparing 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 Mixtures
Comments

Mixtures of Multiple Scaled Distributions
Overview
Mixture of Multiple Scaled t-Distributions
Mixture of Multiple Scaled SAL Distributions
Mixture of Multiple Scaled Generalized Hyperbolic Distributions
Mixture 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

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Author(s)

Biography

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.

Featured Author Profiles

Author - Paul David McNicholas
Author

Paul David McNicholas

Professor & Canada Research Chair, McMaster University
Hamilton, Ontario, Canada

Learn more about Paul David McNicholas »

Reviews

"This Monograph, “Mixture Model-Based Classification” is an excellent book, highly relevant to every statistician working with classification problems."
~International Society for Clinical Biostatistics

 "This monograph is an extensive introduction of mixture models with applications in classification and clustering. . . The author did good work by organizing the materials in a very natural way as well as presenting methods and algorithms in great detail. Moreover, many case studies help the reader understand and appreciate the methodologies presented."
~Journal of the American Statistical Association

"I would recommend this book to anyone interested in learning about application of mixture models to classification problems."
~The International Biometric Society