Branch-and-Bound Applications in Combinatorial Data Analysis

Springer Science & Business Media, Mar 22, 2006 - Mathematics - 222 pages
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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