One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in Euclidean space. A strict linear separation is widely known and is reduced to a linear programming problem. We introduce a strict polynomial separation and show that the strict polynomial separation of two sets also is reduced to a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can only be zero or one. It is zero if the sets are strictly polynomially separable; otherwise, it is one. We give illustrative examples of strict separation of two sets with the help of two-variable fourth-degree algebraic polynomials on the plane. We also analyze the efficiency of applying the strict polynomial separation to binary classification problems.
|Translated title of the contribution||Strict polynomial separation of two sets|
|Journal||ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ|
|Publication status||Published - 2019|
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