Compact integer-programming models for extracting subsets of stimuli from confusion matrices

作     者：Brusco, MJ Stahl, S 

作者机构：Florida State Univ Coll Business Dept Mkt Tallahassee FL 32306 USA 

出 版 物：《PSYCHOMETRIKA》 (心理测量学)

年 卷 期：2001年第66卷第3期

页      面：405-419页

核心收录：

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 04[教育学] 0701[理学-数学] 

主　　题：combinatorial data analysis confusion matrix integer programming 

摘      要：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.