Proximal Knowledge-Based Classification

Abstract

Prior knowledge over general nonlinear sets is incor- porated into proximal nonlinear kernel classification problems as linear equalities. The key tool in this incorporation is the conversion of general nonlinear prior knowledge implications into linear equalities in the classification variables without the need to ker- nelize these implications. These equalities are then included into a proximal nonlinear kernel classifica- tion formulation [1] that is solvable as a system of linear equations. Effectiveness of the proposed formu- lation is demonstrated on a number of publicly avail- able classification datasets. Nonlinear kernel classi- fiers for these datasets exhibit marked improvements upon the introduction of nonlinear prior knowledge compared to nonlinear kernel classifiers that do not utilize such knowledge.