The graph-based clustering aims to utilize structural information from graphs to provide clustering solutions. However, many existing graph clustering methods separate graph construction from the learning of clustering results, and rely on the assumption of consistent feature importance, which often leads to suboptimal clustering outcomes. Anchor-based graph clustering offers an efficient and scalable solution for clustering tasks. Nevertheless, the need to manually specify the number of anchors limits its practicality. Motivated by these issues, this paper proposes a method called Multi-granularity Granular-ball Anchor Graph Clustering with self-weighting (MGAGC). The MGAGC utilizes granular-ball computing to adaptively generate granular-ball anchors based on the data distribution, where the number of granular-ball anchors is much smaller than the number of data samples. Then, by enabling interaction between fine-granularity sample points and coarse-granularity granular-ball anchors in a self-weighting feature space, the MGAGC integrates graph construction with the learning of clustering results. Extensive experiments are conducted on fourteen public datasets to compare the proposed MGAGC with nine classic or state-of-the-art baseline clustering methods. Experimental results show that MGAGC achieves an average ACC of 75.50% and an average NMI of 51.22%, outperforming other clustering methods by an average of 13.60% and 12.21%, respectively. Moreover, statistical test results indicate that its performance differences are statistically significant compared to most of the competing methods. Code is available at https://github.com/awaw-Liyely/2026-IPM-MGAGC . • Adaptive granular-ball anchors auto-counted for full data coverage. • Self-weighted features enable fine-coarse interaction for accurate similarity. • Unified graph-clustering via Laplacian rank gives direct cluster labels. • Experimental results show that the proposed model and algorithm perform well.

Unsupervised feature selection aims to enhance the quality of unlabeled data, thereby improving the performance of subsequent unsupervised learning models. However, most of the existing unsupervised feature selection methods rely on single-granularity modeling, which reduces the expressive capability of data to some extent. In addition, the existing studies are generally based on a forward greedy feature selection strategy, which tends to fall into a local optimum. To address these issues, this paper proposes a novel unsupervised feature selection method for handling hybrid data, called unsupervised feature selection method using fuzzy graph momentum random walk in bi-level granular-ball knowledge space. Specifically, a Bi-level Granular-ball Knowledge Space (BGKS) is first constructed by combining fine granularity and coarse granularity representations through a hybrid Gaussian kernel function. Then, a multi-granularity fuzzy graph is built on the BGKS using upper and lower fuzzy approximation operators. Based on this graph, a Momentum Random Walk (MRW) mechanism is introduced to design the Fuzzy Graph Momentum Random Walk (FGMRW) model. Finally, an iterative unsupervised feature selection algorithm is developed. Extensive experiments on 20 public datasets demonstrate that, compared with existing algorithms, the proposed method is able to maintain or even improve clustering performance while selecting fewer features, thus achieving superior overall performance. The source code of this work is publicly available athttps://github.com/HongtaoGao-code/FGMRW-UFS.