Fast fuzzy clustering via sparse anchor graph with manifold and balance regularizations

Fuzzy C-Means (FCM) clustering has been extensively applied across diverse domains, yet three fundamental challenges persist: (1) the learning process neglects intra-cluster sample distributions, frequently yielding imbalanced or even empty clusters; (2) local geometric structures among samples remain unexploited, failing to preserve intrinsic data relationships; (3) iterative optimization of the full sample-to-center membership matrix incurs substantial computational overhead, making it prohibitive for large-scale datasets. Existing studies have only focused on one or two of the problems. To address the three challenges synergistically, this paper proposes Fast Fuzzy Clustering via Sparse Anchor Graph with Manifold and Balance Regularizations (MB-FFCSAG), which introduces dual regularization constraints on the membership matrix: balance regularization enforces equitable cluster cardinalities, while manifold regularization preserves local neighborhood relationships in membership space, thereby enhancing clustering performance. Crucially, MB-FFCSAG achieves acceleration by learning a anchor-based membership matrix between a small set of anchor points and cluster centers, with sparse anchor graph substituting adjacency graph for manifold preservation. This design renders the method highly scalable to large-scale datasets. Comprehensive evaluations on benchmark datasets validate that MB-FFCSAG achieves significant improvements in clustering performance compared to state-of-the-art fuzzy clustering methods. The code is on the website: https://github.com/LZUFE-Machine-Learning/MB-FFCSAG .