  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.
