Some methods of combining class information in multivariate normal discrimination for the classification of human chromosomes

Abstract

We consider the use of discriminant analysis based on an assumption of multivariate Normality for allocating human chromosomes in an automated system. In this context, the assumptions which might be made about the covariance matrices for the different chromosome classes have important implications for the error rate of the system and the time required to allocate a chromosome. Linear discriminant functions based on the assumption of a common covariance matrix for all classes are fast but sometimes give bigger error rates than the assumption of a separate covariance matrix for each class. The latter assumption requires many more calculations to evaluate the associated quadratic discriminant functions. However, it is possible to assume that the covariance matrices for the different classes are, in various senses, similar to one another in order to derive other methods of combining class information on variability. These methods are here incorporated in the estimative maximum-likelihood approach to discrimination. The methods considered lead to machine classification times of human chromosomes intermediate between those for the assumptions of a common or unrelated covariance matrices. They also require the simultaneous estimation of fewer parameters than the use of a separate covariance matrix for each chromosome class. The methods are illustrated by three data sets of very different quality. Graphs of estimated error rate against classification time show that some of these ways of combining class information can be useful in the trade-off of error rate against time.