SMVCIR: Robust Discriminating (Visualization) Procedures
Western Michigan University
Consider multivariate data composed of k variables (predictors) and g groups with a sample from each group. As a visualization procedure, traditional discriminant analysis offers views of the data based on the space spanned by differences in group means. As discussed, this is essentially the visualization procedure SIR. In this talk, we explore these views in terms of (rank-based) robust estimates. Because visualization is exploratory in nature, procedures based solely on location are limiting. Similar to the traditional procedure SAVE, we expand the spanning space to differences in variances and covariances, based on robust estimates. We further discuss an ordering of the space based on a QR-decomposition of the right unitary matrix of the singular value decomposition of the space. This allows for exploration based on usually a much smaller set of the spanning space. We call the process SMVCIR. Comparisons with SIR and SAVE will be made. Examples and a small simulation study will be discussed. The process can be performed on our web page.