Generalized relative evaluation measure for spectral unmixing

In this paper, we propose novel generalized performance measures for hyperspectral unmixing techniques. Theses generalized relative measures compare two abundances matrices. The first one represents the unmixing result. The second matrix can be either another unmixing result or the ground truth of the hyperspectral scene. These measures start by computing coincidence matrices corresponding to the two abundance matrices. Then, the comparison is carried out by computing statistics of the number of pairs of data points that have high abundances with respect to the same endmember for the first unmixing approach, but have large abundance difference with respect to the same endmember for the second unmixing technique, or large difference in both. The main advantage of this approach is that there is no need to pair the endmembers of the two unmixing approaches. Rather it relies on the assumption that the pixels that are considered as different/same material by one unmixing approach should also be considered different/same material by the other.