Discriminant analysis

Discriminant analysis is an alternative to logistic regression as a method of classification. In discriminant analysis, the predictors are ideally required to be numerical. Discriminant analysis is classified into linear discriminant analysis and quadratic discriminant analysis. This chapter discusses linear discriminant analysis based on Mahalnobis distance. Fisher’s linear discriminant function is an alternative but equivalent way to the Mahalnobis distance function classification rule. The chapter gives a small numerical example to illustrate the calculation of Fisher’s linear discriminating functions and classification. In many applications, the number of predictors, p, is very large and can be even much greater than the sample size. If the predictors are Bernoulli random variables, then their joint multivariate Bernoulli distribution is difficult to model and estimate. In that case, the naive Bayes method ignores the correlations between them and uses the product of Bernoulli probabilities as an approximation.