A Probabilistic Weighted Archetypal Analysis Method with Earth Mover's Distance for Endmember Extraction from Hyperspectral Imagery

A Probabilistic Weighted Archetypal Analysis method with Earth Mover’s Distance (PWAA-EMD) is proposed to extract endmembers from hyperspectral imagery (HSI). The PWAA-EMD first utilizes the EMD dissimilarity matrix to weight the coefficient matrix in the regular Archetypal Analysis (AA). The EMD metric considers manifold structures of spectral signatures in the HSI data and could better quantify the dissimilarity features among pairwise pixels. Second, the PWAA-EMD adopts the Bayesian framework and formulates the improved AA into a probabilistic inference problem by maximizing a joint posterior density. Third, the optimization problem is solved by the iterative multiplicative update scheme, with a careful initialization from the two-stage algorithm and the proper endmembers are finally obtained. The synthetic and real Cuprite Hyperspectral datasets are utilized to verify the performance of PWAA-EMD and five popular methods are implemented to make comparisons. The results show that PWAA-EMD surpasses all the five methods in the average results of spectral angle distance (SAD) and root-mean-square-error (RMSE). Especially, the PWAA-EMD obtains more accurate estimation than AA in almost all the classes of endmembers including two similar ones. Therefore, the PWAA-EMD could be an alternative choice for endmember extraction on the hyperspectral data.