TY - JOUR
AU1 - Malozemov, V.
AU2 - Plotkin, A.
AB - 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.
TI - Strict Polynomial Separation of Two Sets
JF - Vestnik St. Petersburg University: Mathematics
DO - 10.1134/S1063454119020109
DA - 2019-06-11
UR - https://www.deepdyve.com/lp/springer-journals/strict-polynomial-separation-of-two-sets-fg60Ymc7jU
SP - 162
EP - 168
VL - 52
IS - 2
DP - DeepDyve
ER -