We investigate the relationship among several popular end-member extraction algorithms, including N-FINDR, the simplex growing algorithm (SGA), vertex component analysis (VCA), automatic target generation process (ATGP), and fully constrained least squares linear unmixing (FCLSLU). We analyze the fundamental equivalence in the searching criteria of the simplex volume maximization and pixel spectral signature similarity employed by these algorithms. We point out that their performance discrepancy comes mainly from the use of a dimensionality reduction process, a parallel or sequential implementation mode, or the imposition of certain constraints. Instructive recommendations in algorithm selection for practical applications are provided.