A comparison of two methods of discriminant analysis applied to binary data

The results of applying classical linear discriminant analysis and kernel discriminant analysis to several real sets of multivariate binary data are presented. Classical discriminant analysis is intrinsically parametric and is usually presented as being well-suited to continuous variables; it is also well-known to be optimal when the (two) classes have normal distributions with identical covariance matrices. The kernel method, on the other hand, is nonparametric and, in the form used here, is ideally suited to binary data. The apparent error rates of the kernel method are found to be consistently less than those of the classical method. However, when the true error rates are estimated either by applying the classifiers to independent test sets, or by the leaving-one-out method from the design sets, no significant difference is discernible between the two types of classifier.