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To improve the accuracy of spectral analysis for subpixel materials further, a nonlinear unmixing algorithm based on the kernel partial nonnegative matrix factorization (KPNMF) was proposed. Firstly, an endmember extraction algorithm based on the theory of convex geometry was used to generate a candidate pixel set of pure endmembers, and then the pure endmember was determined according to the spatial purity indices of the candidate pixels. Given information of pure endmembers, the kernel method was adopted to extend partial nonnegative matrix factorization (PNMF). The corresponding objective function was constructed, and the iterative solution was also derived to obtain the subpixel endmembers and abundances of all the endmembers. The experimental results demonstrate that the proposed unmixing algorithm has good nonlinear unmixing ability, and the unmixing results are better than those of linear unmixing algorithms. [ABSTRACT FROM AUTHOR]