Parametric linear programming and cluster analysis

Parametric linear programming and cluster analysis

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Article ID: iaor20001174
Country: Netherlands
Volume: 111
Issue: 3
Start Page Number: 582
End Page Number: 588
Publication Date: Dec 1998
Journal: European Journal of Operational Research
Authors: ,
Keywords: lagrange multipliers, programming: integer
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 certin 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. 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.

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