Knowledge-Based Nonlinear Kernel Classifiers

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) classifier. The resulting formulation leads to a linear program that can be solved efficiently. This extends, in a rather unobvious fashion, previous work [3] that incorporated similar prior knowledge into a linear SVM classifier. 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 effectiveness of the proposed approach in generating sharp nonlinear classifiers based mostly or totally on prior knowledge.