Robust linear programming discrimination of two linearly inseparable sets

A single linear programming formulation is proposed which generates a plane that of minimizes an average sum of misclassified points belonging to two disjoint points sets in n-dimensional real space, without the imposition of extraneous normalization constraints that inevitably fail to handle certain cases.

Abstract

A single linear programming formulation is proposed which generates a plane that of minimizes an average sum of misclassified points belonging to two disjoint points sets in n-dimensional real space. When the convex hulls of the two sets are also disjoint, the plane completely separates the two sets. When the convex hulls intersect, our linear program, unlike all previously proposed linear programs, is guaranteed to generate some error-minimizing plane, without the imposition of extraneous normalization constraints that inevitably fail to handle certain cases. The effectiveness of the proposed linear program has been demonstrated by successfully testing it on a number of databases. In addition, it has been used in conjunction with the multisurface method of piecewise-linear separation to train a feed-forward neural network with a single hidden layer.