<p>An orthogonal non-negative matrix factorization model based on graph regularization under noisy conditions (NGONMF) is proposed in this paper. The main result of this paper lies in introducing a noise matrix in the non-negative decomposition process and iteratively updating the noise in the algorithm, and its purpose is to capture the sparsity damage caused by noise or outliers, while using graph regularization terms and orthogonal penalty terms to consider the graph structure information of the data, improving the sparsity of low dimensional representations. At the same time, we have developed corresponding iterative update algorithms and theoretically proved their convergence, which is one of the innovations of this paper. Extensive clustering experiments have been conducted on multiple datasets under the interference of Gaussian noise, non Gaussian noise, and anomalous destruction. The real and reliable empirical results confirm the robustness and competitive advantage of the proposed algorithm. This is another innovation. Therefore, the proposed model can effectively reduce the adverse effects of noise or outliers and obtain robust decomposition results.</p>