Scalable Multi-View Subspace Clustering with Kernel Alignment

In recent years, multi-view subspace clustering (MVSC) has continuously gathered considerable attention for its ability to effectively uncover latent structural information in multi-view data. However, its prohibitive $O( n^{3})$ time complexity undermines its scalability to large-scale data sets. Besides, most of MVSC methods neglect to explore the nonlinear information between data points and anchors. To address both issues simultaneously, we proposes a novel anchor-based method, Scalable Multi-View Subspace Clustering with Kernel Alignment (MVSC-KA), which enhance intra-view nonlinear structural representation through kernel techniques and strengthen the information-capturing capacity of consensus anchor graphs to benefit clustering performance. Specifically, we first integrate anchor graph construction and graph regularization into a unified process, enabling the consensus anchor graph to simultaneously capture global and local information across views while learning view-specific anchor matrices. Gaussian kernel functions are then rationally employed to construct kernel matrices for each view, subsequently fused into a consensus kernel graph. To reinforce latent nonlinear relationships between anchors and data points, we elaborately align the consensus anchor graph with the consensus kernel graph. Finally, a cohesive framework unifies anchor graph construction and kernel alignment for mutual iterative optimization. Extensive experiments on seven public datasets demonstrate that MVSC-KA outperforms state-of-the-art methods, and excels in scalability to large scale data sets.