A new implicit enumeration scheme for the discriminant analysis problem

A new implicit enumeration scheme for the discriminant analysis problem

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Article ID: iaor19951953
Country: United Kingdom
Volume: 22
Issue: 6
Start Page Number: 625
End Page Number: 639
Publication Date: Jul 1995
Journal: Computers and Operations Research
Authors: , ,
Keywords: heuristics, programming: integer
Abstract:

This paper addresses, from a mathematical programming point of view, the problem that consists in determining an hyperplane that separates, as well as possible, two finite sets of points in Rn. In the present formulation, a best separation hyperplane minimizes the number of misclassified points. A new mixed integer formulation of this problem is proposed, together with a solution procedure based on implicit enumeration. The formulation is characterized by a small integrality gap. Extensive numerical results on large scale problems (up to 300 points) are given for both the exact algorithm and a derived heuristic procedure.

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