| Description |
1 online resource (753 pages) |
| Series |
Chapman & Hall/CRC Handbooks of Modern Statistical Methods |
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Chapman & Hall/CRC handbooks of modern statistical methods.
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| Contents |
Front Cover; Contents; Preface; Editors; Contributors; Chapter 1: Cluster Analysis: An Overview; Abstract; 1.1 Introduction; 1.2 Dimensions (Dichotomies) of Clustering; 1.2.1 By Type of Clustering: Hard vs. Soft; 1.2.2 By Type of Clustering: Flat vs. Hierarchical; 1.2.3 By Data Type or Format; 1.2.4 By Clustering Criterion: (Probabilistic) Model-Based vs. Cost-Based; 1.2.5 By Regime: Parametric (K Is Input) vs. Nonparametric (Smoothness Parameter Is Input); 1.3 Types of Clusterings; 1.4 Data Formats; 1.5 Clustering Approaches; 1.5.1 Centroid-Based Clustering |
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1.5.2 Agglomerative Hierarchical Methods1.5.3 Spectral Clustering; 1.5.4 Mixture Probability Models; 1.5.5 Density-Based Clustering; 1.5.6 Other Probability Models; 1.5.7 Further Clustering Approaches; 1.6 Cluster Validation and Further Issues; 1.6.1 Approaches for Cluster Validation; 1.6.2 Number of Clusters; 1.6.3 Variable Selection, Dimension Reduction, Big Data Issues; 1.6.4 General Clustering Strategy and Choice of Method; 1.6.5 Clustering Is Different from Classification; References; Chapter 2: A Brief History of Cluster Analysis; Abstract; 2.1 Introduction; 2.2 Methods |
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2.2.1 Hierarchical Methods2.2.2 Minimal Spanning Tree; 2.2.3 Partitioning Methods; 2.2.4 Mixture Modeling; 2.2.5 Spectral Clustering; 2.3 Applications; 2.4 Surveys of Clustering and an Online Digital Resource; References; Section I: Optimization Methods; Chapter 3: Quadratic Error and k-Means; Abstract; 3.1 Conventional k-Means Clustering; 3.1.1 General; 3.1.2 Three Frameworks for the Square-Error Criterion; 3.2 Equivalent Reformulations of k-Means Criterion; 3.2.1 Anomalous Clustering Criterion; 3.2.2 Inner-Product k-Means Criterion |
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3.2.3 Kernel-Wise Criterion of Maximization of the Semi-Averaged Internal Similarities3.2.4 Spectral Rayleigh Quotient Formulation; 3.3 Challenges for k-Means Criterion and Algorithm; 3.3.1 Properties of the Criterion; 3.3.2 Different Clustering Structures; 3.3.3 Initialization of k-Means; 3.3.4 Getting a Deeper Minimum; 3.3.5 Interpretation Aids; 3.3.6 Feature Weighting, Three-Stage k-Means, and Minkowski Metric; 3.4 Notes on Software for k-Means; Acknowledgments; References; Chapter 4: K-Medoids and Other Criteria for Crisp Clustering; Abstract; 4.1 Introduction; 4.2 K-Medoids |
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4.2.1 The Problem4.2.2 Algorithms; 4.2.3 Choosing the Number of Clusters; 4.2.4 Advantages of K-Medoids; 4.3 Example and Software; 4.3.1 Example: Classifying Animals; 4.3.2 Software Implementations; 4.4 Other Crisp Clustering Methods; 4.4.1 K-Midranges; 4.4.2 K-Modes; 4.5 Conclusion and Open Problems; References; Chapter 5: Foundations for Center-Based Clustering: Worst-Case Approximations and Modern Developments; Abstract; 5.1 Approximation Algorithms for k-Means and k-Median; 5.2 Lloyd's Method for k-Means; 5.3 Properties of the k-Means Objective; 5.4 Local Search-Based Algorithms |
| Summary |
"Handbook of Cluster Analysis provides a comprehensive and unified account of the main research developments in cluster analysis. Written by active, distinguished researchers in this area, the book helps readers make informed choices of the most suitable clustering approach for their problem and make better use of existing cluster analysis tools. The book is organized according to the traditional core approaches to cluster analysis, from the origins to recent developments. After an overview of approaches and a quick journey through the history of cluster analysis, the book focuses on the four major approaches to cluster analysis. These approaches include methods for optimizing an objective function that describes how well data is grouped around centroids, dissimilarity-based methods, mixture models and partitioning models, and clustering methods inspired by nonparametric density estimation. The book also describes additional approaches to cluster analysis, including constrained and semi-supervised clustering, and explores other relevant issues, such as evaluating the quality of a cluster. This handbook is accessible to readers from various disciplines, reflecting the interdisciplinary nature of cluster analysis. For those already experienced with cluster analysis, the book offers a broad and structured overview. For newcomers to the field, it presents an introduction to key issues. For researchers who are temporarily or marginally involved with cluster analysis problems, the book gives enough algorithmic and practical details to facilitate working knowledge of specific clustering areas."--Provided by publisher |
| Notes |
5.4.1 Bounding the Cost of a Swap |
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Print version record |
| Subject |
Cluster analysis.
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Spatial analysis
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Cluster analysis
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| Form |
Electronic book
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| Author |
Meila, Marina
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Murtagh, Fionn
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Rocci, Roberto
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| ISBN |
9781466551893 |
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1466551895 |
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