Strict Polynomial Separation of Two Sets

Abstract

One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in a Euclidean space. Strict linear separation is widely known and reduced to the solution of a linear programming problem. We introduce the notion of strict polynomial separation and show that the strict polynomial separation of two sets can be also reduced to the solution of a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can be only zero or one, i.e., it is zero if the sets admit strict polynomial separation and one otherwise. Some illustrative examples of the strict separation of two sets on a plane with the use of fourth degree algebraic polynomials in two variables are given. The application efficiency of strict polynomial separation to binary data classification problems is analyzed.