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

Abstract Tensor-based multi-view subspace clustering (MVSC) has achieved significant success by capturing high-order inter-view 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 Schatten-p 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.