Align then Tensorize: Multi-Level Consistent Anchor Graph Learning for Scalable Multi-View Clustering

Tensor-based multi-view clustering has been widely studied to capture high-order correlations among multiple views. Nevertheless, existing tensorial methods still exhibit several limitations. First, many approaches rely on full similarity graphs, leading to quadratic or cubic complexity in the number of samples and poor scalability. Second, view-specific anchor graphs are often tensorized without cross-view anchor alignment, yielding structurally inconsistent tensor representations and reduced cross-view comparability. Third, low-rank regularization is typically imposed via the tensor nuclear norm (TNN), which uniformly shrinks singular values and may bias the estimation of the intrinsic tensor rank. To this end, we propose a novel framework, named Align then Tensorize: Multi-level Consistent Anchor Graph Learning for Scalable Multi-View Clustering (ATTMVC). It adopts an anchor-based graph learning framework in which each view is reconstructed from a small set of anchors with sample-wise sparse noise, substantially reducing computational complexity. Unlike existing tensor-based methods that directly tensorize unaligned view-wise anchor graphs, ATTMVC first aligns view-specific anchor graphs into a shared latent space, thereby enforcing structural consistency across views and enabling more reliable modeling of cross-view higher-order correlations. Furthermore, we introduce a Threshold Tensor Rank (TTR) surrogate on the aligned anchor graph tensor, which effectively promotes low-rank structure while mitigating the over-shrinking effect commonly caused by TNN-based regularization. Finally, extensive experiments demonstrate that ATTMVC outperforms state-of-the-art multi-view clustering methods. The code is publicly available at https://github.com/tangchuan2000/ATTMVC.