Branch-and-Bound Applications in Combinatorial Data Analysis [electronic resource] / by Michael J. Brusco, Stephanie Stahl.
Contributor(s): Stahl, Stephanie [author.] | SpringerLink (Online service)Material type: TextSeries: Statistics and Computing: Publisher: New York, NY : Springer New York, 2005Description: XII, 222 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387288109Subject(s): Mathematics | Operations research | Decision making | Management science | Discrete mathematics | Statistics | Mathematics | Discrete Mathematics | Statistics and Computing/Statistics Programs | Operation Research/Decision Theory | Operations Research, Management Science | Statistics for Social Science, Behavorial Science, Education, Public Policy, and LawAdditional physical formats: Printed edition:: No titleDDC classification: 511.1 LOC classification: QA150-272Online resources: Click here to access online
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Cluster Analysis—Partitioning -- 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 -- Seriation -- to the Branch-and-Bound Paradigm for Seriation -- Seriation—Maximization of a Dominance Index -- Seriation—Maximization of Gradient Indices -- Seriation—Unidimensional Scaling -- Seriation—Multiobjective Seriation -- Variable Selection -- to Branch-and-Bound Methods for Variable Selection -- Variable Selection for Cluster Analysis -- Variable Selection for Regression Analysis.
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. 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. Stephanie Stahl is an author and researcher with years of experience in writing, editing, and quantitative psychology research.