Separation via polyhedral conic functions

Abstract

We consider the problem of discriminating between two finite point sets A and B in the n-dimensional space by using a special type of polyhedral function. An effective finite algorithm for finding a separating function based on iterative solutions of linear programming subproblems is suggested. At each iteration a function whose graph is a polyhedral cone with vertex at a certain point is constructed and the resulting separating function is defined as a point-wise minimum of these functions. It has been shown that arbitrary two finite point disjoint sets can be separated by using this algorithm. An illustrative example is given and an application on classification problems with some real-world data sets has been implemented.