FEATURE EXTRACTION AND DATA DISPLAY

This study investigates the area of feature extraction for statistical pattern recognition. The reduction of dimensionality resulting from feature extraction has many benefits. In a lower dimensional space classifier design is usually easier, and computational complexity is reduced. Nonlinear feature extraction for the two class case is investigated first. The goal is to specify a procedure that provides a systematic method to extract features related to the gaussian minus-log-likelihood ratio. A mapping is determined that finds a nonlinear subspace orthogonal to the most recent feature. In the nonlinear subspace a second feature is extracted. If it contributes to increased separability, it is retained and the procedure is iterated. When this is no longer true, the procedure is terminated. Linear feature extraction using a nonparametric approach is investigated next. By generalizing the scatter matrices used in discriminant analysis several new procedures result. The nonparametric discriminant analysis procedure is shown to possess several advantages over the parametric version. An extension is presented for distributional testing. Finally, an additional extension is presented that allows an alternate derivation of the valley seeking clustering algorithm. If only two features are extracted, we can easily plot the data for user observation. It is this two-dimensional display of data that is considered next. The display is developed using nonparametric log densities as a basis. Applications to a wide variety of classifier design problems are presented. In addition a condensing algorithm is presented. If a large number of samples are provided, and it is desired to display the samples, then a procedure is needed to select samples for display. Using nonparametric measures as a basis a new algorithm is determined that selects representative samples