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国际著名数学图书（影印版）：组合数据分析·通过动态规划进行优化（英文版）

国际著名数学图书（影印版）：组合数据分析·通过动态规划进行优化（英文版）

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作者: [美] 休伯特著

出版社: 清华大学出版社

出版时间: 2011-02

版次: 1

ISBN: 9787302245018

定价: 25.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 163页

分类: 自然科学

2 张插图图片

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.
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
内容简介:
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

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