Schroedinger eigenmaps with knowledge propagation for target detection

Abstract

The applicability of Laplacian Eigenmaps (LE) and Schroedinger Eigenmaps (SE) has been widely shown in the processing of hyperspectral imagery. Specifically, we have previously shown that SE has a promising performance in spectral target detection. SE, unlike LE, could include prior information or labeled data points into a barrier potential term that steers the transformation in certain directions making the labeled points and the similar points pulled toward the origin in the new space. We have also noticed that the barrier potentials generated from a few labeled points may affect in a brittle manner the dimensionality in the Schroedinger space and in turn, the target detection performance. In this paper, we show that the number of SE used in the detection could be increased without affecting the detection performance by adding spatial and spectral constraints on the individual labeled points and propagating this knowledge to nearby points through a modified Schroedinger matrix. We apply our algorithm to hyperspectral data sets with several target panels and different complexity in order to have a wide framework of assessment.