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.

中文翻译：

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用于数据表示的全变分约束图正则化凸非负矩阵分解


我们提出了一种新颖的 NMF 算法，称为总变分约束图正则化凸非负矩阵分解（TV-GCNMF），将总变分和图拉普拉斯与凸 NMF 结合起来。在该模型中，数据的特征细节通过基于梯度信息的扩散系数来保存。图正则化和凸约束揭示了特征的内在几何和结构信息；从而获得稀疏和基于部分的表示。此外，我们给出了乘法更新规则并证明了所提出算法的收敛性。在各种噪声条件下对多个数据集进行的聚类实验结果表明，与最先进的聚类方法和其他相关工作相比，该方法的有效性和鲁棒性。