Graph-regularized representation methods have demonstrated promising performance in image clustering. However, with the exponential growth of image data scales, traditional graph-regularized methods are no longer efficient in handling large-scale datasets due to their high computational and spatial complexity. Due to both natural and non-natural factors, real-world application data often contain outliers. To address these issues, this paper proposes a Bipartite graph-regularized robust Low-rank Matrix Factorization (BLMF) method for semi-supervised image clustering. The bipartite graph structure reduces the computational complexity to \(\varvec{O(ndt)}\) , representing a significant improvement compared to traditional graph-regularized methods with computational complexity of \(\varvec{O(n}^{\varvec{2}}\varvec{dt)}\) . Furthermore, to mitigate the negative effects of outliers, the Maximum Correntropy Criterion (MCC) is introduced as a fidelity measure in constructing the optimization model. Additionally, we propose an anchor point selection strategy to reduce the influence of anchor outliers. An iterative algorithm based on Fenchel Conjugate (FC) and Block Coordinate Update (BCU) techniques is developed to solve our model effectively. The convergence properties of the proposed algorithm are rigorously analyzed, demonstrating that it satisfies both objective convergence and iterative sequential convergence. Experiments are conducted on 11 real image datasets, comparing the proposed BLMF method with 12 state-of-the-art algorithms. The results demonstrate that the proposed method outperforms competing methods in most cases across small, medium, and large datasets.
