Finding a Subset of Stimulus-Response Pairs with Minimum Total Confusion: A Binary Integer Programming Approach

Abstract

Confusion matrices are a convenient and widely accepted means of tabulating results from experiments in which subjects choose responses to various stimuli. This paper is relevant to studies in which the recognition and confusability characteristics of a large set of possible stimuli are tested in order to select the smaller subset of stimuli that will eventually be presented to the user (e.g., selecting sculpted pushbuttons or command words for voice-interactive systems). Rather than applying cluster analyses, this paper demonstrates how to formulate optimization models from the information contained in a confusion matrix. Four binary integer programming models are proposed that when solved, yield the subset of stimuli exhibiting minimum total confusion. The models are solvable using widely available software on a microcomputer. A sizable example from the literature is solved and discussed, and directions for algorithmic research are recommended.