Localized Exploratory Projection Pursuit

Based on CART, we introduce a recursive partitioning method for high dimensional space which partitions the data using low dimensional features. The low dimensional features are extracted via an exploratory projection pursuit (EPP) method, localized to each node in the tree. In addition, we present an exploratory splitting rule that is potentially less biased to the training data. This leads to a nonparametric classifier for high dimensional space that has local feature extractors optimized to different regions in the input space. 1 Introduction Due to the curse of dimensionality (Bellman, 1961) it is desirable to extract features from a high dimensional data space before attempting a classification. This may be done in those cases where the important structure is assumed to lie in a low dimensional subspace of the original data. The most well know method for extracting features is principal components, however it has been argued that these features may not retain the structure needed..