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Non-negative matrix factorization (NMF) approximates a non-negative matrix by the product of two low-rank matrices and achieves good performance in clustering. Recently, semi-supervised NMF (SS-NMF) further improves the performance by incorporating part of the labels of few samples into NMF. In this paper, we proposed a novel graph based SS-NMF (GSS-NMF). For each sample, GSS-NMF minimizes its distances to the same labeled samples and maximizes the distances against different labeled samples to incorporate the discriminative information. Since both labeled and unlabeled samples are embedded in the same reduced dimensional space, the discriminative information from the labeled samples is successfully transferred to the unlabeled samples, and thus it greatly improves the clustering performance. Since the traditional multiplicative update rule converges slowly, we applied the well-known projected gradient method to optimizing GSS-NMF and the proposed algorithm can be applied to optimizing other manifold regularized NMF efficiently. Experimental results on two popular document datasets, i.e., Reuters21578 and TDT-2, show that GSS-NMF outperforms the representative SS-NMF algorithms.