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The p-Median Problem for Cluster Analysis: A Comparative Test Using the Mixture Model Approach

Author

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  • T. D. Klastorin

    (Graduate School of Business, University of Washington, Seattle, Washington 98195)

Abstract

Recently, Mulvey and Crowder (Mulvey, J., H. Crowder. 1979. Cluster analysis: an application of Lagrangian relaxation. Management Sci. 25 329--340.) suggested that the p-median problem might be useful for cluster analysis problems (where the goal is to group objects described by a vector of characteristics in such a way that objects in the same group are somehow more alike than objects in different groups). The intent of this paper is to test Mulvey and Crowder's proposal using the mixture model approach; i.e., by applying a number of algorithms (including one for the p-median problem) to a set of objects randomly sampled from a number of known multivariate populations and comparing the ability of each algorithm to detect the original populations. In order to evaluate the results, a generalized partition comparison measure and its distribution are developed. Using this measure, results from various algorithms are compared.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:1:p:84-95
    DOI: 10.1287/mnsc.31.1.84
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    Citations

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    Cited by:

    1. Benati, Stefano & García, Sergio, 2012. "A p-median problem with distance selection," DES - Working Papers. Statistics and Econometrics. WS ws121913, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.
    3. Michael Brusco & Douglas Steinley, 2015. "Affinity Propagation and Uncapacitated Facility Location Problems," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 443-480, October.
    4. Simon Blanchard & Daniel Aloise & Wayne DeSarbo, 2012. "The Heterogeneous P-Median Problem for Categorization Based Clustering," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 741-762, October.
    5. Michael Brusco & Hans-Friedrich Köhn, 2009. "Exemplar-Based Clustering via Simulated Annealing," Psychometrika, Springer;The Psychometric Society, vol. 74(3), pages 457-475, September.
    6. Antiopi Panteli & Basilis Boutsinas & Ioannis Giannikos, 2021. "On solving the multiple p-median problem based on biclustering," Operational Research, Springer, vol. 21(1), pages 775-799, March.
    7. Vakharia, Asoo J. & Mahajan, Jayashree, 2000. "Clustering of objects and attributes for manufacturing and marketing applications," European Journal of Operational Research, Elsevier, vol. 123(3), pages 640-651, June.
    8. Michael Brusco & Hans-Friedrich Köhn, 2009. "Clustering Qualitative Data Based on Binary Equivalence Relations: Neighborhood Search Heuristics for the Clique Partitioning Problem," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 685-703, December.
    9. Huerta-Muñoz, Diana L. & Ríos-Mercado, Roger Z. & Ruiz, Rubén, 2017. "An iterated greedy heuristic for a market segmentation problem with multiple attributes," European Journal of Operational Research, Elsevier, vol. 261(1), pages 75-87.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.

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