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E-grāmata: Mixture Model-Based Classification

5.00/5 (4 ratings by Goodreads)
(McMaster University)
  • Formāts: 236 pages
  • Izdošanas datums: 04-Oct-2016
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781315356112
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Mixture Model-Based ClassificationPalielināt
  • Formāts: 236 pages
  • Izdošanas datums: 04-Oct-2016
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781315356112
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"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.

Recenzijas

"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

List of Figures
xiii
List of Tables
xvii
Preface xxiii
1 Introduction
1(10)
1.1 Classification
1(2)
1.2 Finite Mixture Models
3(1)
1.3 Model-Based Clustering, Classification, and Discriminant Analysis
4(2)
1.4 Comparing Partitions
6(2)
1.5 R Packages
8(1)
1.6 Datasets
9(1)
1.7 Outline of the Contents of This Monograph
9(2)
2 Mixtures of Multivariate Gaussian Distributions
11(28)
2.1 Historical Development
11(3)
2.2 Parameter Estimation
14(6)
2.2.1 Model-Based Clustering
14(1)
2.2.2 Model-Based Classification
15(2)
2.2.3 Model-Based Discriminant Analysis
17(1)
2.2.4 Initialization via Deterministic Annealing
18(1)
2.2.5 Stopping Rules
18(2)
2.3 Gaussian Parsimonious Clustering Models
20(4)
2.4 Model Selection
24(1)
2.5 Merging Gaussian Components
25(2)
2.6 Illustrations
27(9)
2.6.1 x2 Data
27(2)
2.6.2 Banknote Data
29(2)
2.6.3 Female Voles Data
31(2)
2.6.4 Italian Olive Oil Data
33(3)
2.7 Comments
36(3)
3 Mixtures of Factor Analyzers and Extensions
39(24)
3.1 Factor Analysis
39(4)
3.1.1 The Model
39(1)
3.1.2 An EM Algorithm for the Factor Analysis Model
40(2)
3.1.3 Woodbury Identity
42(1)
3.1.4 Comments
43(1)
3.2 Mixture of Factor Analyzers
43(1)
3.3 Parsimonious Gaussian Mixture Models
44(5)
3.3.1 A Family of Eight Models
44(1)
3.3.2 Parameter Estimation
44(4)
3.3.3 Comments
48(1)
3.4 Expanded Parsimonious Gaussian Mixture Models
49(3)
3.4.1 A Family of Twelve Models
49(1)
3.4.2 Parameter Estimation
50(2)
3.5 Mixture of Common Factor Analyzers
52(3)
3.5.1 The Model
52(1)
3.5.2 Parameter Estimation
52(3)
3.5.3 Discussion
55(1)
3.6 Illustrations
55(6)
3.6.1 x2 Data
55(1)
3.6.2 Italian Wine Data
56(2)
3.6.3 Italian Olive Oil Data
58(1)
3.6.4 Alon Colon Cancer Data
59(2)
3.7 Comments
61(2)
4 Dimension Reduction and High-Dimensional Data
63(16)
4.1 Implicit and Explicit Approaches
63(1)
4.2 PGMM Family in High-Dimensional Applications
64(1)
4.3 VSCC
65(2)
4.4 Clustvarsel and selvarclust
67(1)
4.5 GMMDR
68(1)
4.6 HD-GMM
69(2)
4.7 Illustrations
71(5)
4.7.1 Coffee Data
71(1)
4.7.2 Leptograpsus Crabs
71(3)
4.7.3 Banknote Data
74(1)
4.7.4 Wisconsin Breast Cancer Data
74(1)
4.7.5 Leukaemia Data
75(1)
4.8 Comments
76(3)
5 Mixtures of Distributions with Varying Tail Weight
79(20)
5.1 Mixtures of Multivariate t-Distributions
79(3)
5.2 Mixtures of Power Exponential Distributions
82(7)
5.3 Illustrations
89(5)
5.3.1 Overview
89(1)
5.3.2 x2 Data
89(1)
5.3.3 Body Data
89(1)
5.3.4 Diabetes Data
90(2)
5.3.5 Female Voles Data
92(1)
5.3.6 Leptograpsus Crabs Data
93(1)
5.4 Comments
94(5)
6 Mixtures of Generalized Hyperbolic Distributions
99(24)
6.1 Overview
99(1)
6.2 Generalized Inverse Gaussian Distribution
99(2)
6.2.1 A Parameterization
99(1)
6.2.2 An Alternative Parameterization
100(1)
6.3 Mixtures of Shifted Asymmetric Laplace Distributions
101(5)
6.3.1 Shifted Asymmetric Laplace Distribution
101(1)
6.3.2 Parameter Estimation
102(2)
6.3.3 SAL Mixtures versus Gaussian Mixtures
104(2)
6.4 Mixture of Generalized Hyperbolic Distributions
106(5)
6.4.1 Generalized Hyperbolic Distribution
106(2)
6.4.2 Parameter Estimation
108(3)
6.5 Mixture of Generalized Hyperbolic Factor Analyzers
111(4)
6.5.1 The Model
111(1)
6.5.2 Parameter Estimation
111(3)
6.5.3 Analogy with the Gaussian Solution
114(1)
6.6 Illustrations
115(4)
6.6.1 Old Faithful Data
115(1)
6.6.2 Yeast Data
116(2)
6.6.3 Italian Wine Data
118(1)
6.6.4 Liver Data
118(1)
6.7 A Note on Normal Variance-Mean Mixtures
119(1)
6.8 Comments
120(3)
7 Mixtures of Multiple Scaled Distributions
123(16)
7.1 Overview
123(1)
7.2 Mixture of Multiple Scaled t-Distributions
124(2)
7.3 Mixture of Multiple Scaled SAL Distributions
126(1)
7.4 Mixture of Multiple Scaled Generalized Hyperbolic Distributions
127(1)
7.5 Mixture of Coalesced Generalized Hyperbolic Distributions
128(1)
7.6 Cluster Convexity
129(3)
7.7 Illustrations
132(5)
7.7.1 Bankruptcy Data
132(1)
7.7.2 Other Clustering Examples
133(2)
7.7.3 Classification and Discriminant Analysis Examples
135(2)
7.8 Comments
137(2)
8 Methods for Longitudinal Data
139(18)
8.1 Modified Cholesky Decomposition
139(1)
8.2 Gaussian Mixture Modelling of Longitudinal Data
140(8)
8.2.1 The Model
140(1)
8.2.2 Model Fitting
141(1)
8.2.2.1 VEA Model
141(3)
8.2.2.2 EVI Model
144(1)
8.2.3 Constraining Sub-Diagonals of Tg
145(1)
8.2.3.1 VdEA Model
145(2)
8.2.3.2 EdVI Model
147(1)
8.2.4 Modelling the Component Means
147(1)
8.3 Using t-Mixtures
148(2)
8.4 Illustrations
150(6)
8.4.1 Clustering
150(3)
8.4.2 Classification
153(3)
8.5 Comments
156(1)
9 Miscellania
157(24)
9.1 On the Definition of a Cluster
157(2)
9.2 What Is the Best Way to Perform Clustering, Classification, and Discriminant Analysis?
159(3)
9.3 Mixture Model Averaging
162(2)
9.4 Robust Clustering
164(2)
9.5 Clustering Categorical Data
166(2)
9.6 Cluster-Weighted Models
168(1)
9.7 Mixed-Type Data
169(3)
9.7.1 A Mixture of Latent Variables Model
169(1)
9.7.2 Illustration: Urinary System Disease Diagnosis
170(2)
9.8 Alternatives to the EM Algorithm
172(2)
9.8.1 Variational Bayes Approximations
172(1)
9.8.2 Other Approaches
173(1)
9.9 Challenges and Open Questions
174(3)
Appendix 177(4)
A.1 Linear Algebra Results
177(1)
A.2 Matrix Calculus Results
178(1)
A.3 Method of Lagrange Multipliers
179(2)
References 181(24)
Index 205
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.
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