In high-dimensional data, one often seeks a few interesting low-dimensional projections which reveal important aspects of the data. Projection pursuit is a procedure for searching high-dimensional data for interesting low-dimensional projections via the optimization of a criterion function called the projection pursuit index. Very few projection pursuit indices incorporate class or group information in the calculation, and hence can be adequately applied to supervised classification problems. We introduce new indices derived from linear discriminant analysis that can be used for exploratory supervised classification.;When we have the small number of observations relative to the number of variables, the class structure of optimal projection can be biased too much. In this situation, most of classical multivariate analysis methods also be problematic, too. We discuss how the sample size and dimensionality are related, and we propose a new projection pursuit index that considers the penalty for the projection coefficients and overcomes the small number of observation problem.
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