THE NONLINEAR DISCRIMINANT AND STEPWISE NONLINEAR DISCRIMINANT ANALYSES

The nonlinear discriminant function, when covariance matrixes of each population are not equal to each other, is discussed on the basis of Bayes’ criterion, and by using the stepwise discriminant method, a method for calculating the nonlinear discriminant function is provided, which is called "stepwise nonlinear discriminant analysis". In addition, an appropriate discriminant analysis model is selected by testing whether the covariance matrixes of each population are equal, which was proposed by Box. The calculations show that, the discriminant effects of this method are superior not only to linear discriminant analysis, but also to nonlinear discriminant analysis in which the stepwise discriminant algorithm is not used when covariance matrixes of each population are not equal to each other. Satisfactory results have been obtained in applying this method. This is an important improvement on the linear discriminant analysis used in the weather typing prediction at present.