A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

The analysis and interpretation of datasets with large number of features and few examples has remained as a challenging problem in the scientific community, owing to the difficulties associated with the curse-of-the-dimensionality phenomenon. Projection Pursuit (PP) has shown promise in circumventing this phenomenon by searching low-dimensional projections of the data where meaningful structures are exposed. However, PP faces computational difficulties in dealing with datasets containing thousands of features (typical in genomics and proteomics) due to the vast quantity of parameters to optimize. In this paper we describe and evaluate a PP framework aimed at relieving such difficulties and thus ease the construction of classifier systems. The framework is a two-stage approach, where the first stage performs a rapid compaction of the data and the second stage implements the PP search using an improved version of the SPP method (Guo et al., 2000, 32). In an experimental evaluation with eight public microarray datasets we showed that some configurations of the proposed framework can clearly overtake the performance of eight well-established dimension reduction methods in their ability to pack more discriminatory information into fewer dimensions.