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 inter-view correlations. However, existing approaches face two principal limitations. First, most methods either exclusively emphasize the inter-view $\textbf{low‑rankness}$ (R) prior while neglecting the intra-view $\textbf{local-smoothness}$ (S) prior, or treat R and S as two separate regularizers—complicating joint optimization. Second, conventional $\textbf{tensor‑based}$ 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 $\textit{Unified View Extraction with Low‑Rankness and Smoothness Fusion (UVELRS)}$ method. Our framework first extracts a consistent cross‑view representation and then constructs a tensor by stacking these representations. We introduce a novel $\textit{tensor total variation Schatten p-norm}$ 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. We provide the source code of UVELRS in the supplementary material.