A p-median problem with distance selection
AbstractThis paper introduces an extension of the p-median problem and its application to clustering, in which the distance/dissimilarity function between units is calculated as the distance sum on the q most important variables. These variables are to be chosen from a set of m elements, so a new combinatorial feature has been added to the problem, that we call the p-median model with distance selection. This problem has its origin in cluster analysis, often applied to sociological surveys, where it is common practice for a researcher to select the q statistical variables they predict will be the most important in discriminating the statistical units before applying the clustering algorithm. Here we show how this selection can be formulated as a non-linear mixed integer optimization mode and we show how this model can be linearized in several different ways. These linearizations are compared in a computational study and the results outline that the radius formulation of the p-median is the most efficient model for solving this problem.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws121913.
Date of creation: Jun 2012
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p-median problem; Distance selection; Radius formulation;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-08 (All new papers)
- NEP-CMP-2012-07-08 (Computational Economics)
- NEP-ECM-2012-07-08 (Econometrics)
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- Stefano Benati & Silvana Stefani, 2011. "The Academic Journal Ranking Problem: A Fuzzy-Clustering Approach," Journal of Classification, Springer, vol. 28(1), pages 7-20, April.
- John M. Mulvey & Harlan P. Crowder, 1979. "Cluster Analysis: An Application of Lagrangian Relaxation," Management Science, INFORMS, vol. 25(4), pages 329-340, April.
- T. D. Klastorin, 1985. "The p-Median Problem for Cluster Analysis: A Comparative Test Using the Mixture Model Approach," Management Science, INFORMS, vol. 31(1), pages 84-95, January.
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