Parametric discriminant development

Parametric discriminant development methods employ the mean vectors and covariance matrices of each class of data to develop the separating discriminant. Linear discriminant analysis (LDA), based on Bayesian statistics, generates a linear discriminant function with the following form ... 

The literature of multivariate classification shows that several types of methods have found utility in application to chemical problems. Excellent discussions of the major methods can be found in Strouf ° and Tou and Gon-zalez. The most frequently used methods include parametric approaches involving linear and quadratic discriminant analysis based on the Bayesian approach,nonparametric linear discriminant development methods,and those methods based on principal components analysis such as SIMCA (Soft Independent Modeling by Class Analogy). 

The COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) procedure, developed by Lewis and co-workers [92], uses a form of discriminant analysis based on two descriptors, namely, molecular planarity and electronic activation energy (the difference between the energies of the highest occupied and lowest unoccupied molecular orbitals), which predict the potential of a compound to act as a substrate for one of the cytochromes P450. Lewis et al. [93] found 64% correct predictions for 100 compounds tested by the NTP for mutagenicity. 

The most popular and widely used parametric method for pattern recognition is discriminant analysis. The background to the development and use of this technique will be illustrated using a simple bivariate example. 

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