The standard NMF algorithm is not suitable for sampling data from low-dimensional manifolds embedded in high-dimensional environmental spaces, as the geometric information hidden in feature manifolds and sample manifolds is rarely learned. In order to obtain better clustering performance based on NMF, manifold and orthogonal constraint, a new type of model named Orthogonal Graph regularized Non-negative Matrix Factorization model under Sparse Constraints (OGNMFSC) is proposed. Firstly, this type of model constructs a nearest neighbor graph to encode the geometric information of the data space, in order to obtain more discriminative ability by preserving the structure of the graph. Secondly, this type of model adds orthogonal constraints to achieve better local representation and significantly reduce the inconsistency between the original matrix and the basis vectors. Thirdly, by adding sparse constraints to obtain a sparser representation matrix, the clustering performance of the model can be improved. The main conclusion of this paper is that two effective algorithms have been generated to solve the model, which not only provides theoretical convergence proof for these two algorithms, but also demonstrates significant clustering performance in experiments compared to classical models such as K-means, PCA, NMF, Semi-NMF, NMFSC, ONMF, GNMF, NeNMF.

中文翻译：

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稀疏约束下的正交图正则化非负矩阵分解聚类

标准NMF算法不适合从嵌入高维环境空间的低维流形中采样数据，因为隐藏在特征流形和样本流形中的几何信息很少被学习。为了获得基于NMF、流形和正交约束的更好的聚类性能，提出了一种新型模型——稀疏约束下的正交图正则化非负矩阵分解模型（OGNMFSC）。此类模型首先构造最近邻图来编码数据空间的几何信息，以便通过保留图的结构来获得更多的判别能力。其次，此类模型增加了正交约束，以实现更好的局部表示，并显着减少原始矩阵和基向量之间的不一致。第三，通过添加稀疏约束以获得更稀疏的表示矩阵，可以提高模型的聚类性能。本文的主要结论是生成了两种有效的算法来求解模型，不仅为这两种算法提供了理论上的收敛证明，而且在实验中与K-means、PCA等经典模型相比表现出了显着的聚类性能、NMF、半 NMF、NMFSC、ONMF、GNMF、NeNMF。