Kernel Stochastic Separation Theorems and Separability Characterizations of Kernel Classifiers

Ivan Yu. Tyukin, Alexander N. Gorban, Bogdan Grechuk, Stephen Green

Abstract: In this work we provide generalizations and extensions of stochastic separation theorems to kernel classifiers. A general separability result for two random sets is also established. We show that despite feature maps corresponding to a given kernel function may be infinite-dimensional, kernel separability characterizations can be expressed in terms of finite-dimensional volume integrals. These integrals allow to determine and quantify separability properties of an arbitrary kernel function. The theory is illustrated with numerical examples.