On detecting nonlinear patterns in discriminant problems

  • Authors:
  • Chih-Yang Tsai

  • Affiliations:
  • School of Business, The State University of New York at New Paltz, 75 South Manheim Blvd., New Paltz, NY 12561, USA

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2006

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Abstract

We propose a two-stage model for detecting nonlinear patterns in discriminant problems and for solving the problem. The model deploys a Linear Programming Based Discriminator (LPBD) in stage one for treating linear patterns and a Probabilistic Neural Network (PNN) in stage two for handling nonlinear patterns. The LPBD in stage one divides the decision space into a clear zone where observations are (almost) linearly separable and a gray zone where nonlinear patterns are more likely to occur. The PNN in stage two analyzes the gray zone and determines whether a significant nonlinear patterns exist in the observations. Our goal is to avoid using a nonlinear model unless the PNN strongly suggests so to maintain good interpretability and avoid overfitting. Our computational study demonstrates the effectiveness of the two-stage model in both classification accuracy and computational efficiency.