Abstract
BackgroundWhen comparing diseased and non-diseased patients in order to discriminate between the aspects associated with the specific disease, it is often observed that the diseased patients have more variability than the non-diseased patients. In such cases Quadratic discriminant analysis is required which is based on the estimation of different covariance structures for the different groups. Having different covariance matrices means the Canonical variate transformation cannot be used to obtain a visual representation of the discrimination and group separation.ResultsIn this paper an alternative method is proposed: combining the different transformations for the different groups into a single representation of the sample points with classification regions. In order to associate the differences in variables with group discrimination, a biplot is produced which include information on the variables, samples and their relationship.
Highlights
When comparing diseased and non-diseased patients in order to discriminate between the aspects associated with the specific disease, it is often observed that the diseased patients have more variability than the non-diseased patients
It is shown in Appendix A that classification of a sample is to the nearest canonical mean in the Canonical variate analysis (CVA) biplot when the prior probabilities are equal and for unequal prior probabilities, a quantity of log(πj) is added to the distance to the j-th class mean
In cases where the variance between groups differs, Quadratic discriminant analysis (QDA) should be applied with the estimation of different covariance matrices for different groups
Summary
When comparing diseased and non-diseased patients in order to discriminate between the aspects associated with the specific disease, it is often observed that the diseased patients have more variability than the non-diseased patients. As the prefix ‘bi-’ suggests, both the samples and variables of a data matrix is represented in a biplot.
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