Kernel Spectral Angle Mapper

This communication introduces a very simple generalization of the familiar spectral angle mapper (SAM) distance. SAM is perhaps the most widely used distance in chemometrics, hyperspectral imaging, and remote sensing applications.  We show that a nonlinear version of SAM can be readily obtained by measuring the angle between pairs of vectors in a reproducing kernel Hilbert spaces. The kernel SAM generalizes the angle measure to higher-order statistics, it is a valid reproducing kernel, it is universal, and it has consistent geometrical properties that permit deriving a metric easily. We illustrate its performance in a target detection problem using very high resolution imagery. Excellent results and insensitivity to parameter tuning over competing methods make it a valuable choice for many applications.