<p>Graph-based semi-supervised non-negative matrix factorization achieves promising performance in dimension reduction owing to its powerful data representation capability, which preserves the local geometric structure of the sample data. Existing methods focus on the efficiency derived from the respective contributions of the structural features of labeled and unlabeled data, thereby failing to fully exploit the intrinsic connections between their structural information components. Furthermore, existing graph fusion methods concentrate more on these strategies for constructing graphs from multiple information sources rather than on how to filter duplicate information to improve the quality of the fusion graph. For these reasons, a semi-supervised non-negative matrix factorization via adaptive high-order graph controllable fusion (AGFSNMF) is proposed. Specifically, by constructing a label projection matrix, an improved label propagation mechanism is designed to establish the latent structural relationships propagated from unlabeled data to the labeled field. This mechanism alleviates the inaccuracy and inefficiency issues arising from the pseudo-label matrices typically inherited from conventional label propagation mechanisms. Moreover, to flexibly incorporate the most appropriate graph subsets, an adaptive selective fusion strategy is developed to adaptively select multiple high-order similarity graphs according to their individual contributions, such that the discriminative power is enhanced with an effective and appropriate balance between leveraging high-order information and eliminating fusion redundancy. The superiority of the proposed method is validated through extensive experiments on ten benchmark datasets, demonstrating a maximum average improvement of 11.63% in clustering accuracy over the baseline methods.</p>