Mixture Model-Based Classification: 1st Edition (Hardback) book cover

Mixture Model-Based Classification

1st Edition

By Paul D. McNicholas

Chapman and Hall/CRC

212 pages | 38 B/W Illus.

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Hardback: 9781482225662
pub: 2016-08-19
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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.

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

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

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General