Non-negative matrix factorization (NMF) is a critical technique in the field of data clustering, and its developments typically revolve around two main directions: enhancing the model’s ability to preserve the intrinsic geometric structure of data, and improving the quality of learned features by imposing constraints such as orthogonality or sparsity. However, most existing methods, when integrating these two approaches, overlook a potential issue: enforcing orthogonality or sparsity constraints based on an imprecise geometric structure described by a first-order graph may inadvertently distort the true manifold structure of the data. To address this fundamental conflict, we propose a novel Sparse Higher-order Dual Graph Regularized Orthogonal Non-negative Matrix Factorization (SO-DHNMF) method. Its core innovation lies in introducing a higher-order graph regularization term capable of capturing second-order nearest-neighbor relationships, thereby providing a more robust and precise topological foundation for orthogonality and sparsity constraints. As a result, these constraints synergistically enhance each other rather than conflict. Furthermore, we derive efficient multiplicative update rules for the proposed model and provide a theoretical proof of its convergence. Experimental results on three real-world datasets demonstrate that the proposed SO-DHNMF method achieves superior performance compared to several classical clustering methods in image clustering tasks.