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Spectral mixture analysis has been an important research topic in remote sensing applications, particularly for hyperspectral remote sensing data processing. On the basis of linear spectral mixture models, this paper applied directed and weighted graphs to describe the relationship between pixels. In particular, we transformed the endmember extraction problem in the decomposition of mixed pixels into an issue of optimization and built feasible solution space to evaluate the practical significance of the objective function, thereby establishing two ant colony optimization algorithms for endmember extraction. In addition to the detailed process of calculation, we also addressed the effects of different operating parameters on algorithm performance. Finally we designed two sets of simulation data experiments and one set of actual data experiments, and the results of those experiments prove that endmember extraction based on ant colony algorithms can avoid some defects of N-FINDR, VCA and other algorithms, improve the representation of endmembers for all image pixels, decrease the average value of root-mean-square error, and therefore achieve better endmember extraction results than the N-FINDR and VCA algorithms.