Unsupervised hyperspectral image analysis with projection pursuit

Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyperspectral images does not always coincide with such projections. We propose an application of projection pursuit (PP), which seeks to find a set of projections that are “interesting,” in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two-step iterative process is followed where we first search for a projection that maximizes a projection index based on the information divergence of the projection’s estimated probability distribution from the Gaussian distribution and then reduce the rank by projecting the data onto the subspace orthogonal to the previous projections. To calculate each projection, we use a simplified approach to maximizing the projection index, which does not require an optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of this method is demonstrated through simulated examples as well as data from the hyperspectral digital imagery collection experiment (HYDICE) and the spatially enhanced broadband array spectrograph system (SEBASS).