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Compact Integer-Programming Models for Extracting Subsets of Stimuli from Confusion Matrices

Published online by Cambridge University Press:  01 January 2025

Michael J. Brusco  and
Stephanie Stahl
Michael J. Brusco*
Affiliation:
Marketing Department, Florida State University
Stephanie Stahl
Affiliation:
Tallahassee, Florida
*
Requests for reprints should be sent to Michael J. Brusco, Marketing Department, College of Business, Florida State University, Tallahassee, FL 32306-1110. E-Mail: mbrusco@cob.fsu.edu
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Abstract

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.

Keywords

combinatorial data analysisconfusion matrixinteger programming
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 405 - 419
Copyright
Copyright © 2001 The Psychometric Society

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