Parametric linear programming and cluster analysis

Parametric linear programming and cluster analysis In the cluster analysis problem one seeks to partition a finite set of objects into disjoint groups (or clusters) such that each group contains relatively similar objects and, relatively dissimilar objects are placed in different groups. For certain classes of the problem or, under certain assumptions, the partitioning exercise can be formulated as a sequence of linear programs (LPs), each with a parametric objective function. Such LPs can be solved using the parametric linear programming procedure developed by Gass and Saaty ((Gass, S., Saaty, T. (1955), Naval Research Logistics Quarterly 2, 39–45)). In this paper, a parametric linear programming model for solving cluster analysis problems is presented. We show how this model can be used to find optimal solutions for certain variations of the clustering problem or, in other cases, for an approximation of the general clustering problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png European Journal of Operational Research Elsevier

Parametric linear programming and cluster analysis

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Publisher
Elsevier
Copyright
Copyright © 1998 Elsevier Science B.V.
ISSN
0377-2217
eISSN
1872-6860
D.O.I.
10.1016/S0377-2217(97)00379-2
Publisher site
See Article on Publisher Site

Abstract

In the cluster analysis problem one seeks to partition a finite set of objects into disjoint groups (or clusters) such that each group contains relatively similar objects and, relatively dissimilar objects are placed in different groups. For certain classes of the problem or, under certain assumptions, the partitioning exercise can be formulated as a sequence of linear programs (LPs), each with a parametric objective function. Such LPs can be solved using the parametric linear programming procedure developed by Gass and Saaty ((Gass, S., Saaty, T. (1955), Naval Research Logistics Quarterly 2, 39–45)). In this paper, a parametric linear programming model for solving cluster analysis problems is presented. We show how this model can be used to find optimal solutions for certain variations of the clustering problem or, in other cases, for an approximation of the general clustering problem.

Journal

European Journal of Operational ResearchElsevier

Published: Dec 16, 1998

References

  • Optimal sequential partitions of graphs
    Kernighan, B.

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