Supervised and Unsupervised Spectral Angle Classifiers

Abstract

We report that the cosine of the angle 6 (spectral angle) can be utilized as a metric for measuring distances in feature space for multispectral image classification and clustering. Due to the invariant nature of the cosine of the angle 8 to the linearly scaled variations, when two spectra are exactly linearly scaled variations of one another by distance r, the cosine of the angle B becomes zero while spectral distance is scaled by r. The fact that the cosine of the angle B becomes zero when two spectra are exactly linearly scaled variations of one another implies that if we only have spectral patterns that are exactly linearly scaled variations of one another, then we will not be able to define distances between pairs of signatures for classification and clustering. For this reason, the cosine of the angle has never been considered before as a metric for multispectral