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Cluster Analysis: An Application of Lagrangian Relaxation

  • John M. Mulvey

    (Princeton University)

  • Harlan P. Crowder

    (IBM T. J. Watson Research Center)

Registered author(s):

    This paper presents and tests an effective optimization algorithm for clustering homogeneous data. The algorithm iteratively employs a subgradient method for determining lower bounds and a simple search procedure for determining upper bounds. The overall objective is to assign n objects to m mutually exclusive "clusters" such that the sum of the distances from each object to a designated cluster median is minimum. The model represents a special case of the uncapacitated facility location and m-median problems. This technique has proven efficient for examples with n \le 200 (i.e., the number of 0-1 variables \le 40,000); computational experiences with 10 real-world clustering applications are provided. A comparison with a hierarchical agglomerative heuristic, the minimum squared error method, is included. It is shown that the optimization algorithm is an effective solution technique for the homogeneous clustering problem, and also a good method for providing tight lower bounds for evaluating the quality of solutions generated by other procedures.

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    File URL: http://dx.doi.org/10.1287/mnsc.25.4.329
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 25 (1979)
    Issue (Month): 4 (April)
    Pages: 329-340

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    Handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:329-340
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