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Keywords:

  • prior knowledge;
  • kernel classification;
  • proximal support vector machines

Abstract

Prior knowledge over general nonlinear sets is incorporated 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 kernelize these implications. These equalities are then included into a proximal nonlinear kernel classification formulation (G. Fung and O. L. Mangasarian, Proximal support vector machine classifiers, in Proceedings KDD-2001: Knowledge Discovery and Data Mining, F. Provost and R. Srikant (eds), San Francisco, CA, New York, Association for Computing Machinery) that is solvable as a system of linear equations. Effectiveness of the proposed formulation is demonstrated on a number of publicly available classification datasets. Nonlinear kernel classifiers for these datasets exhibit marked improvements upon the introduction of nonlinear prior knowledge compared with nonlinear kernel classifiers that do not utilize such knowledge. Copyright © 2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1: 000-000, 2009