Abstract: We propose a robust nonnegative matrix factorization on manifold via projected gradient method. The proposed algorithm utilizes the L₂₁ norm to measure the quality of factorization, which is insensitive to noise and outliers. The proposed algorithm also utilizes the geometrical structure of the dataset and considers the local invariance. Therefore, it combines manifold learning with the nonnegative matrix factorization. We utilize the projected gradient method to obtain updating rules. Experimental results on several datasets and comparisons with several other clustering algorithms demonstrate the effectiveness of the proposed algorithm.