Kernel spectral angle mapper

This communication introduces a very simple generalisation of the familiar spectral angle mapper (SAM) distance. SAM is perhaps the most widely used distance in chemometrics, hyperspectral imaging, and remote sensing applications. It is shown 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 generalises 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.