Knowledge-Based Nonlinear Kernel Classi ers

Abstract

Prior knowledge in the form of multiple polyhedral sets, each belonging to one of two categories, is introduced into a reformulation of a nonlinear kernel support vector machine (SVM) classi er. The resulting formulation leads to a linear program that can be solved e ciently. This extends, in a rather unobvious fashion, previous work [3] that incorporated similar prior knowledge into a linear SVM classi er. Numerical tests on standard-type test problems, such as exclusive-or prior knowledge sets and a checkerboard with 16 points and prior knowledge instead of the usual 1000 points, show the e ectiveness of the proposed approach in generating sharp nonlinear classi ers based mostly or totally on prior knowledge.