Optimal partitioning of a data set based on the p-median model

Michael J. Brusco, Hans Friedrich Köhn

Research output: Contribution to journalArticle

Abstract

Although the K-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The p-median model is an especially well-studied clustering problem that requires the selection of p objects to serve as cluster centers. The objective is to choose the cluster centers such that the sum of the Euclidean distances (or some other dissimilarity measure) of objects assigned to each center is minimized. Using 12 data sets from the literature, we demonstrate that a three-stage procedure consisting of a greedy heuristic, Lagrangian relaxation, and a branch-and-bound algorithm can produce globally optimal solutions for p-median problems of nontrivial size (several hundred objects, five or more variables, and up to 10 clusters). We also report the results of an application of the p-median model to an empirical data set from the telecommunications industry.

Original languageEnglish (US)
Pages (from-to)89-105
Number of pages17
JournalPsychometrika
Volume73
Issue number1
DOIs
StatePublished - Mar 1 2008
Externally publishedYes

Keywords

  • Branch and bound
  • Cluster analysis
  • Combinatorial data analysis
  • Heuristics
  • Lagrangian relaxation
  • P-median problem

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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