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Considering a wide range of applications of nonnegative matrix factorization (NMF), many NMF and their variants have been developed. Since previous NMF methods cannot fully describe complex inner global and local manifold structures of the data space and extract complex structural information, we propose a novel NMF method called dual-graph global and local concept factorization (DGLCF). To properly describe the inner manifold structure, DGLCF introduces the global and local structures of the data manifold and the geometric structure of the feature manifold into CF. The global manifold structure makes the model more discriminative, while the two local regularization terms simultaneously preserve the inherent geometry of data and features. Finally, we analyze convergence and the iterative update rules of DGLCF. We illustrate clustering performance by comparing it with latest algorithms on four real-world datasets.

We propose a novel NMF algorithm, named Total Variation constrained Graph-regularized Convex Non-negative Matrix Factorization (TV-GCNMF), to incorporate total variation and graph Laplacian with convex NMF. In this model, the feature details of the data are preserved by a diffusion coefficient based on the gradient information. The graph regularization and convex constraints reveal the intrinsic geometry and structure information of the features; thereby, obtaining sparse and parts-based representations. Furthermore, we give the multiplicative update rules and prove convergence of the proposed algorithm. The results of clustering experiments on multiple datasets, under various noise conditions, show the effectiveness and robustness of the proposed method compared to state-of-the-art clustering methods and other related work.