Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities

The study of human performance on discrete optimization problems has a considerable history that spans various disciplines. The purpose of this paper is to outline a program of study for the measurement of human performance on discrete optimization problems related to clustering of points in the two-dimensional plane. I describe possible objective criteria for clustering problems, the measurement of agreement of solutions produced by subjects, and categories of experiments for investigating human performance on clustering problems. To facilitate future experimental testing of human subjects on clustering problems, optimal partitions were obtained for 233 two-dimensional clustering problems ranging in size from 10 to 70 points. For each test problem, an optimal solution was obtained for each of three objective criteria: (a) maximizing partition split, (b) minimizing partition diameter, and (c) minimizing within-cluster sums of squares, and similarity of the solutions among these criteria has been computed.