Combinatorial data analysis:optimization by dynamic programming
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作 者：Lawrence Hubert，Phipps Arabie，Jacqueline Meulman著
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ISBN：9787302245018
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简介
Combinatorial data analysis (CDA) refers to a wide class of
methods for the study of relevant data sets in which the
arrangement of a collection of objects is absolutely central.
Combinatorial Data Analysis: Optimization by Dynamic Programming
focuses on the identification of arrangements, which are then
further restricted to where the combinatorial search is carried
out by a recursive optimization process based on the general
principles of dynamic programming (DP).
The authors provide a comprehensive and self-contained review
delineating a very general DP paradigm, or schema, that can serve
two functions. First, the paradigm can be applied in various
special forms to encompass all previously proposed applications
suggested in the classification literature. Second, the paradigm
can lead directly to many more novel uses. An appendix is
included as a user's manual for a collection of programs
available as freeware.
The incorporation of a wide variety of CDA tasks under one
common optimization framework based on DP is one of this book's
strongest points. The authors include verifiably optimal
solutions to nontrivially sized problems over the array of data
analysis tasks discussed.
This monograph provides an applied documentation source, as
well as an introduction to a collection of associated computer
programs, that will be of interest to applied statisticians and
data analysts as well as notationally sophisticated users.
目录
Preface
1 Introduction
2 General Dynamic Programming Paradigm
2.1 An Introductory Example: Linear Assignment
2.2 The GDPP
3 Cluster Analysis
3.1 Partitioning
3.1.1 Admissibility Restrictions on Partitions
3.1.2 Partitioning Based on Two-Mode Proximity Matrices
3.2 Hierarchical Clustering
3.2.1 Hierarchical Clustering and the Optimal Fitting of Ultrametrics
3.2.2 Constrained Hierarchical Clustering
4 Object Sequencing and Seriation
4.1 Optimal Sequencing of a Single Object Set
4.1.1 Symmetric One-Mode Proximity Matrices
4.1.2 Skew-Symmetric One-Mode Proximity Matrices
4.1.3 Two-Mode Proximity Matrices
4.1.4 Object Sequencing for Symmetric One-Mode Proximity Matrices Based on the Construction of Optimal Paths
4.2 Sequencing an Object Set Subject to Precedence Constraints
4.3 Construction of Optimal Ordered Partitions
5 Heuristic Applications of the GDPP
5.1 Cluster Analysis
5.2 Object Sequencing and Seriation
6 Extensions and Generalizations
6.1 Introduction
6.1.1 Multiple Data Sources
6.1.2 Multiple Structures
6.1.3 Uses for the Information in the SetsΩ1,...,Ωk
6.1.4 A Priori Weights for Objects and/or Proximities
6.2 Prospects
Appendix: Available Programs
Bibliography
Author Index
Subject Index
1 Introduction
2 General Dynamic Programming Paradigm
2.1 An Introductory Example: Linear Assignment
2.2 The GDPP
3 Cluster Analysis
3.1 Partitioning
3.1.1 Admissibility Restrictions on Partitions
3.1.2 Partitioning Based on Two-Mode Proximity Matrices
3.2 Hierarchical Clustering
3.2.1 Hierarchical Clustering and the Optimal Fitting of Ultrametrics
3.2.2 Constrained Hierarchical Clustering
4 Object Sequencing and Seriation
4.1 Optimal Sequencing of a Single Object Set
4.1.1 Symmetric One-Mode Proximity Matrices
4.1.2 Skew-Symmetric One-Mode Proximity Matrices
4.1.3 Two-Mode Proximity Matrices
4.1.4 Object Sequencing for Symmetric One-Mode Proximity Matrices Based on the Construction of Optimal Paths
4.2 Sequencing an Object Set Subject to Precedence Constraints
4.3 Construction of Optimal Ordered Partitions
5 Heuristic Applications of the GDPP
5.1 Cluster Analysis
5.2 Object Sequencing and Seriation
6 Extensions and Generalizations
6.1 Introduction
6.1.1 Multiple Data Sources
6.1.2 Multiple Structures
6.1.3 Uses for the Information in the SetsΩ1,...,Ωk
6.1.4 A Priori Weights for Objects and/or Proximities
6.2 Prospects
Appendix: Available Programs
Bibliography
Author Index
Subject Index
Combinatorial data analysis:optimization by dynamic programming
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