Low-Rank Smooth Unified Anchor Tensor Nonnegative Orthogonal Factorization for Multi-view Clustering

Anchor-based tensor learning provides an efficient framework for large-scale multi-view clustering by combining compact anchor representations with high-order cross-view modeling. However, existing methods often rely on predefined anchors, separating anchor construction from subsequent tensor learning and preventing their joint optimization. Moreover, independently learned anchors in heterogeneous feature spaces may lack explicit cross-view correspondence, while conventional low-rank tensor regularization tends to overlook local smoothness among samples. To address these limitations, we propose a $\text{L}$ow-Rank $\text{S}$mooth $\text{U}$nified $\text{A}$nchor $\text{T}$ensor $\text{N}$onnegative $\text{O}$rthogonal $\text{F}$actorization ($\text{LS-UATNOF}$) model for multi-view clustering. Specifically, heterogeneous views are projected into a common feature space, where a unified anchor matrix is adaptively learned and shared across all views. Unlike two-stage schemes, the unified anchors and tensor representations are jointly optimized, allowing the high-order structure revealed by tensor factorization to feed back into anchor learning. Tensor total variation Schatten-$p$ regularization is further incorporated to capture global low-rankness and sample-wise local smoothness within a single term. An efficient ADMM-based optimization algorithm is developed. Extensive experiments on eight benchmark datasets demonstrate that $\text{LS-UATNOF}$ achieves competitive or superior clustering performance with favorable convergence and computational efficiency.