Optimal Partitioning of a Data Set Based on the "p"-Median Model

Autor/inn/en	Brusco, Michael J.; Kohn, Hans-Friedrich
Titel	Optimal Partitioning of a Data Set Based on the "p"-Median Model
Quelle	In: Psychometrika, 73 (2008) 1, S.89-105 (17 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-007-9021-4
Schlagwörter	Telecommunications; Item Response Theory; Multivariate Analysis; Heuristics; Mathematical Models + Suchen Sie Ihr Suchwort? Telekommunikationstechnik; Item-Response-Theorie; Multivariate Analyse; Heuristik; Mathematical model; Mathematisches Modell
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. (Author).
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Update	2017/4/10