Synthesis of Nonlinear Decision Boundaries by Cascaded Threshold Gates

Abstract—This paper presents a technique for generating a nonlinear decision surface that separates two finite classes of elements in n-dimensional real space. It incorporates the principle of cascaded threshold gates in evolving the required separation surface. At each stage of the design, an additional cascaded gate is added which will separate at least one new element. Necessary and sufficient conditions are developed whereby one may readily determine if two new elements may be properly separated by the addition of one cascaded threshold gate. The results are illustrated by means of numerical examples.