A Fast Endmember Extraction Algorithm Based on Gram Determinant

In the field of endmember extraction, most methods involve calculating the volume of simplex in high-dimensional space. Two different simplex volume formulas are used in these methods. One requires dimensionality reduction (DR); therefore, it may result in loss of the information of targets classes with a low priori probability, such as that used in N-FINDR. The other one, which is based on Gram determinant, avoids DR but is time consuming. In this letter, we explain a recursion rule of the calculation for the second simplex volume. Based on that rule, this letter presents a fast endmember extraction algorithm named as Fast Gram Determinant based Algorithm (FGDA). The theoretical analysis and experiments on both simulated and real hyperspectral data demonstrate that, compared to other volume-based methods, FGDA can greatly reduce the computational complexity of endmember extraction.