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The Optimal Classification Using a Linear Discriminant for Two Point Classes Having Known Mean and Covariance


  • Cooke, Tristrom
  • Peake, Michael


The current study provides a simple algorithm for finding the optimal ROC curve for a linear discriminant between two point distributions, given only information about the classes' means and covariances. The method makes no assumptions concerning the exact type of distribution and is shown to provide the best possible discrimination for any physically reasonable measure of the classification error. This very general solution is shown to specialise to results obtained in other papers which assumed multi-dimensional Gaussian distributed classes, or minimised the maximum classification error. Some numerical examples are provided which show the improvement in classification of this method over previously used methods.

Suggested Citation

  • Cooke, Tristrom & Peake, Michael, 2002. "The Optimal Classification Using a Linear Discriminant for Two Point Classes Having Known Mean and Covariance," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 379-394, August.
  • Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:379-394

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    Cited by:

    1. Cooke, Tristrom, 2004. "A lower bound on the performance of the quadratic discriminant function," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 371-383, May.


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