Fast multi-view clustering via smooth low-rank tensor learning

Multi-view clustering aims to learn a consistent clustering structure by utilizing complementary information across different feature views, but balancing discriminative representation learning and computational efficiency remains challenging. Existing anchor-based tensor methods exploit high-order cross-view correlations to improve representation learning. However, suppressing localized noise perturbations while preserving dominant structural components and correcting semantic inconsistency across heterogeneous views are issues that remain insufficiently addressed. In addition, some methods still rely on spectral clustering post-processing on the sample graph, which incurs extra computational and storage overhead and restricts their scalability on large datasets. To address these limitations, we propose Fast Multi-view Clustering via Smooth Low-Rank Tensor Learning (FSLR-MVC). Specifically, we first integrates smooth nonconvex low-rank regularization into anchor tensor learning, enabling the model to adaptively preserve the dominant structural information of the anchor graphs while suppressing local noise perturbations. Next, anchor-guided geometric regularization further incorporates the geometric relationships among anchors into the representation learning process, thereby improving the structural reliability of the learned anchor graphs. Subsequently, we employ cross-view semantic alignment learning to map the view-specific anchor graphs into a shared consensus representation, thereby reconciling the heterogeneous semantics across different views. Finally, FSLR-MVC directly performs k-means on the consensus representation without constructing an n×n sample affinity matrix or conducting corresponding spectral decomposition. The overall computational complexity of the algorithm grows linearly with the number of samples, providing favorable scalability for large-scale datasets. Experimental results on several benchmark datasets show that FSLR-MVC achieves competitive clustering performance while maintaining high computational efficiency.