Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization constraints. GNMF has demonstrated exceptional performance in clustering and dimensionality reduction, effectively discovering inherent low-dimensional structures embedded within high-dimensional spaces. However, the sensitivity of GNMF to noise limits its stability and robustness in practical applications. In order to enhance feature sparsity and mitigate the impact of noise while mining row sparsity patterns in the data for effective feature selection, we introduce the $\ell_{2,0}$-norm constraint as the sparsity constraints for GNMF. We propose an unsupervised feature learning framework based on GNMF\_$\ell_{20}$ and devise an algorithm based on PALM and its accelerated version to address this problem. Additionally, we establish the convergence of the proposed algorithms and validate the efficacy and superiority of our approach through experiments conducted on both simulated and real image data.

基于GNMF和l2,0范数约束的非负矩阵分解方法，旨在提取具有稀疏特征、减轻噪音影响的数据低维结构，通过实验验证了算法的有效性和优越性。

基于图正则化的L20范数非负矩阵分解的无监督特征学习