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Nonnegative matrix factorization (NMF) is one of the most popular data representation methods in the field of computer vision and pattern recognition. High-dimension data are usually assumed to be sampled from the submanifold embedded in the original high-dimension space. To preserve the locality geometric structure of the data, k-nearest neighbor (k-NN) graph is often constructed to encode the near-neighbor layout structure. However, k-NN graph is based on Euclidean distance, which is sensitive to noise and outliers. In this article, we propose a refined-graph regularized nonnegative matrix factorization by employing a manifold regularized least-squares regression (MRLSR) method to compute the refined graph. In particular, each sample is represented by the whole dataset regularized with ℓ2-norm and Laplacian regularizer. Then a MRLSR graph is constructed based on the representative coefficients of each sample. Moreover, we present two optimization schemes to generate refined-graphs by employing a hard-thresholding technique. We further propose two refined-graph regularized nonnegative matrix factorization methods and use them to perform image clustering. Experimental results on several image datasets reveal that they outperform 11 representative methods. [ABSTRACT FROM AUTHOR]