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 datasets. Besides, most of MVSC methods neglect to explore the nonlinear information between data points and anchors. To address both issues simultaneously, we propose a novel anchor-based method, scalable multi-view subspace clustering with kernel alignment (MVSC-KA), prior similarity knowledge among original data points through kernel techniques to enhance the ability to capture nonlinear structures within each view, and employ consensus anchor graphs to strengthen cross-view information integration, thereby effectively improving clustering performance. Specifically, we first integrated 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. Subsequently, considering that original data typically exhibit nonlinear distributions in high-dimensional spaces, we introduced Gaussian kernel functions to construct kernel matrices for each view. This approach embeds nonlinear prior structural information between original data points and further enables the acquisition of a consistent kernel graph through kernel fusion. To reinforce latent nonlinear relationships between anchors and data points, we elaborately aligned the consensus anchor graph with the consensus kernel graph. Finally, a cohesive framework unified 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 datasets.
