Visualization and graphics can play an important role in understanding discriminant analysis. Fisher's canonical variates provide a graphical counterpart to linear discriminant analysis (LDA). For quadratic discriminant analysis (QDA) there is no standard graphical representation, although some dimension reduction methods have been discussed in the literature. In this contribution we propose a graphical method to be used in conjunction with model-based mixture discriminant analysis. Depending on the number of mixture components for each class and the adopted intraclass covariance matrices, the estimated subspace is able to show the main geometric characteristics of the fitted mixture model. The proposal reduces to the usual Fisher' canonical variates when a single mixture component with common intraclass covariance matrix is used. If the intraclass covariance matrices are unconstrained, the estimated subspace is equivalent to that provided by SAVE, a graphical method proposed for use in QDA.
Graphical Tools for Model-based Mixture Discriminant Analysis
SCRUCCA, Luca
2012
Abstract
Visualization and graphics can play an important role in understanding discriminant analysis. Fisher's canonical variates provide a graphical counterpart to linear discriminant analysis (LDA). For quadratic discriminant analysis (QDA) there is no standard graphical representation, although some dimension reduction methods have been discussed in the literature. In this contribution we propose a graphical method to be used in conjunction with model-based mixture discriminant analysis. Depending on the number of mixture components for each class and the adopted intraclass covariance matrices, the estimated subspace is able to show the main geometric characteristics of the fitted mixture model. The proposal reduces to the usual Fisher' canonical variates when a single mixture component with common intraclass covariance matrix is used. If the intraclass covariance matrices are unconstrained, the estimated subspace is equivalent to that provided by SAVE, a graphical method proposed for use in QDA.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.