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Matrix Reorganization and Dynamic Programming: Applications to Paired Comparisons and Unidimensional Seriation

Published online by Cambridge University Press:  01 January 2025

L. J. Hubert  and
R. G. Golledge
L. J. Hubert*
Affiliation:
The University of California, Santa Barbara
R. G. Golledge*
Affiliation:
The University of California, Santa Barbara
*
Requests for reprints should be sent to either L. J. Hubert, Graduate School of Education, University of California, Santa Barbara, California 93106 or R. G. Golledge, Department of Geography, University of California, Santa Barbara, California 93106.
Requests for reprints should be sent to either L. J. Hubert, Graduate School of Education, University of California, Santa Barbara, California 93106 or R. G. Golledge, Department of Geography, University of California, Santa Barbara, California 93106.
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Abstract

A recursive dynamic programming strategy is discussed for optimally reorganizing the rows and simultaneously the columns of an n × n proximity matrix when the objective function measuring the adequacy of a reorganization has a fairly simple additive structure. A number of possible objective functions are mentioned along with several numerical examples using Thurstone's paired comparison data on the relative seriousness of crime. Finally, the optimization tasks we propose to attack with dynamic programming are placed in a broader theoretical context of what is typically referred to as the quadratic assignment problem and its extension to cubic assignment.

Keywords

combinatorial optimizationquadratic assignmentcubic assignment
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 429 - 441
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

Partial support for this research was provided by NIJ Grant 80-IJ-CX-0061.

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