Nonlinear Knowledge-Based Classification

Abstract

Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification problems as linear constraints in a linear program. The key tool in this incorporation is a theorem of the alternative for convex functions that converts nonlinear prior knowledge implications into linear inequalities without the need to kernelize these implications. Effectiveness of the proposed formulation is demonstrated on three publicly available classification datasets, including a cancer prognosis dataset. Nonlinear kernel classifiers for these datasets exhibit marked improvements upon the introduction of nonlinear prior knowledge compared to nonlinear kernel classifiers that do not utilize such knowledge.