Branch-and-Bound Applications in Combinatorial Data Analysis

Michael J. Brusco, Stephanie Stahl - Collection Statistics and Computing

220 pages, parution le 08/09/2005

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Résumé

There are a variety of combinatorial optimization problems that are relevant to the examination of statistical data. Combinatorial problems arise in the clustering of a collection of objects, the seriation (sequencing or ordering) of objects, and the selection of variables for subsequent multivariate statistical analysis such as regression. The options for choosing a solution strategy in combinatorial data analysis can be overwhelming. Because some problems are too large or intractable for an optimal solution strategy, many researchers develop an over-reliance on heuristic methods to solve all combinatorial problems. However, with increasingly accessible computer power and ever-improving methodologies, optimal solution strategies have gained popularity for their ability to reduce unnecessary uncertainty. In this monograph, optimality is attained for nontrivially sized problems via the branch-and-bound paradigm.

For many combinatorial problems, branch-and-bound approaches have been proposed and/or developed. However, until now, there has not been a single resource in statistical data analysis to summarize and illustrate available methods for applying the branch-and-bound process. This monograph provides clear explanatory text, illustrative mathematics and algorithms, demonstrations of the iterative process, psuedocode, and well-developed examples for applications of the branch-and-bound paradigm to important problems in combinatorial data analysis. Supplementary material, such as computer programs, are provided on the world wide web.

L'auteur - Michael J. Brusco

Dr. Brusco is a Professor of Marketing and Operations Research at Florida State University, an editorial board member for the Journal of Classification, and a member of the Board of Directors for the Classification Society of North America.

L'auteur - Stephanie Stahl

Stephanie Stahl is an author and researcher with years of experience in writing, editing, and quantitative psychology research.

Sommaire

An Introduction to Branch-and-Bound Methods for Partitioning
Minimum-Diameter Partitioning
Minimum Within-Cluster Sums of Dissimilarities Partitioning
Minimum Within-Cluster Sums of Squares Partitioning
Multiobjective Partitioning
Introduction to the Branch-and-Bound Paradigm for Seriation
Maximization of a Dominance Index
Seriation--Maximization of Gradient Indices
Seriation--Unidimensional Scaling
Seriation--Multiobjective Seriation
An Introduction to Branch-and-Bound Methods for Variable Selection
Variable Selection for Cluster Analysis
Variable Selection for Regression Analysis

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michael J. Brusco, Stephanie Stahl
Collection	Statistics and Computing
Parution	08/09/2005
Nb. de pages	220
Format	16 x 24
Couverture	Broché
Poids	460g
Intérieur	Noir et Blanc
EAN13	9780387250373
ISBN13	978-0-387-25037-3