A lower bound on the performance of the quadratic discriminant function

  • Authors:

  • Tristrom Cooke

  • Affiliations:

  • Cooperative Research Centre for Sensor Signals and Information Processing, SPRI Building, 1 Mawson Lakes Boulevard, Mawson Lakes, S.A. 5095, Australia

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2004

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Abstract

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.