A triplot for multiclass classification visualisation

Quadratic discriminant analysis is used when the assumption of equal covariance matrices for linear discrimination does not hold. The Canonical Variate Analysis biplot is used for graphical visualisation to accompany linear discriminant analysis. However, since class specific covariance matrix estimates are needed for quadratic discrimination the canonical transformation cannot be used. An alternative method of visually representing the discrimination and classification process is proposed: representing the sample points, classification regions based on quadratic discriminant analysis and including information on the variables. The methodology is further extended to other forms of multiclass classification and illustrated for support vector machines, classification trees, k-nearest neighbours and latent class analysis. In all these triplots three aspects are represented simultaneously, allowing for the representation of the relationships between samples and variables, relative to the classification regions.