Random subspaces and SAR classification efficacy

The 'curse of dimensionality' has limited the application of statistical modeling techniques to low-dimensional spaces, but typical data usually resides in high-dimensional spaces (at least initially, for instance images represented as arrays of pixel values). Indeed, approaches such as Principal Component Analysis and Independent Component Analysis attempt to extract a set of meaningful linear projections while minimizing interpoint distance distortions. The counterintuitive yet effective random projections approach of Johnson and Lindenstrauss defines a sample-based dimensionality reduction technique with probabilistically provable distortion bounds. We investigate and report on the relative efficacy of two random projection techniques for Synthetic Aperture Radar images in a classification setting.