Unified View Extraction with Low-Rankness and Smoothness Fusion for Multi-View Subspace Clustering

Tensor-based multi-view subspace clustering (MVSC) has achieved significant success by capturing high-order interview correlations. However, existing approaches face two principal limitations. First, most methods either exclusively emphasize the inter-view low-rankness (R) prior while neglecting the intra-view local smoothness (S) prior, or treat R and S as two separate regularizers-complicating joint optimization. Second, conventional tensor-based methods impose only low-rank constraints on the representation tensor, which limits their ability to simultaneously model consistency and complementary information. To address these issues, we propose a Unified View Extraction with Low-Rankness and Smoothness Fusion (UVELRS) method. Our framework first extracts a consistent cross-view representation and then constructs a tensor by stacking these representations. We introduce a novel tensor total variation Schattenp norm that simultaneously encodes both R and S priors while offering flexible singular-value control. This unified formulation effectively captures both high-order inter-view correlations and intra-view local smoothness. Extensive experiments on real-world datasets demonstrate UVELRS's superior performance and robustness.