IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v25y1979i4p329-340.html
   My bibliography  Save this article

Cluster Analysis: An Application of Lagrangian Relaxation

Author

Listed:
  • John M. Mulvey

    (Princeton University)

  • Harlan P. Crowder

    (IBM T. J. Watson Research Center)

Abstract

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.

Suggested Citation

  • John M. Mulvey & Harlan P. Crowder, 1979. "Cluster Analysis: An Application of Lagrangian Relaxation," Management Science, INFORMS, vol. 25(4), pages 329-340, April.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:329-340
    DOI: 10.1287/mnsc.25.4.329
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.25.4.329
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.25.4.329?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:329-340. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.