An analytical expression for the error rate associated with the quadratic discriminant function

Abstract

The estimation of the error rates is of vital importance in classification problems, as this is used as a basis to choose the best discriminant function, i.e. the one with a minimum misclassification error.

The quadratic discriminant function (QDF) has been in use for a long time for the purpose of classification. However, there is no exact analytical expression for the misclassification error rate based on QDF. Consequently, researchers depend on use of simulation trials to gauge the misclassification error. This paper provides exact formulae for the misclassification error rates associated with QDF involving two multivariate normal populations. The results are obtained for the general case where the means and the covariance matrices for the two populations are unequal.

Keywords:

• misclassification error
• multivariate normal distribution
• quadratic discriminant function