Visualisation of quadratic discriminant analysis and its application in exploration of microbial interactions

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. 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.

In 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.