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Nonlinear Knowledge in Kernel Machines

Olvi Mangasarian
Mathematics, UCSD


Prior knowledge over arbitrary general sets is incorporated intononlinear support vector machine approximation and classificationproblems as linear constraints of a linear program. The key tool inthis incorporation is a theorem of the alternative for convexfunctions that converts nonlinear prior knowledge implications intolinear inequalitieswithout the need to kernelize these implications. Effectiveness of theproposed formulation is demonstrated on synthetic examples and onimportant breast cancer prognosis problems. All these problemsexhibit marked improvements upon the introduction of prior knowledgeover nonlinear kernel approaches that do not utilizesuch knowledge.

Tuesday, April 24, 2007
11:00AM AP&M 2402