The Heterogeneous P-Median Problem for Categorization Based Clustering

Abstract

The p-median offers an alternative to centroid-based clustering algorithms for identifying unobserved categories. However, existing p-median formulations typically require data aggregation into a single proximity matrix, resulting in masked respondent heterogeneity. A proposed three-way formulation of the p-median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures. Three proposed heuristics for the heterogeneous p-median (HPM) are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major U.S. retailers, as well as through a Monte Carlo analysis.

Keywords: p-median, heterogeneity, sorting task, categorization, clustering, consumer psychology

JEL Classification: C6, C60, M31, M30