Branch-and-Bound Applications in Combinatorial Data Analysis

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Springer Science & Business Media, Mar 22, 2006 - Mathematics - 222 pages
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This monograph focuses on the application of the solution strategy known as branch-and-bound to problems of combinatorial data analysis. Combinatorial data analysis problems typically require either the sel- tion of a subset of objects from a larger (master) set, the grouping of a collection of objects into mutually exclusive and exhaustive subsets, or the sequencing of objects. To obtain verifiably optimal solutions for this class of problems, we must evaluate (either explicitly or implicitly) all feasible solutions. Unfortunately, the number of feasible solutions for problems of combinatorial data analysis grows exponentially with pr- lem size. For this reason, the explicit enumeration and evaluation of all solutions is computationally infeasible for all but the smallest problems. The branch-and-bound solution method is one type of partial enume- tion solution strategy that enables some combinatorial data analysis pr- lems to be solved optimally without explicitly enumerating all feasible solutions. To understand the operation of a branch-and-bound algorithm, we d- tinguish complete solutions from partial solutions. A complete solution is one for which a feasible solution to the optimization problem has been produced (e. g. , all objects are assigned to a group, or all objects are - signed a sequence position). A partial solution is an incomplete solution (e. g. , some objects are not assigned to a group, or some objects are not assigned a sequence position).
 

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Contents

Introduction
1
Cluster AnalysisPartitioning
9
Partitioning
25
Minimum WithinCluster Sums of Dissimilarities Partitioning
43
Minimum WithinCluster Sums of Squares Partitioning
59
6
77
Introduction to the BranchandBound Paradigm for Seriation
91
9
113
Variable Selection
171
13
177
21
183
Variable Selection for Regression Analysis
186
32
192
General BranchandBound Algorithm
203
38
213
177
218

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