SLR-MVTC: Smooth Low-Rank Multi-View Tensor Clustering

Multi-view tensor clustering (MVTC) has gained much attention for its effectiveness in capturing global high-order correlations across views. However, current MVTC methods suffer from two limitations: 1) adopting a two-stage process to learn the latent features for clustering, and 2) either ignoring local similarities within views or treating local similarities and global high-order correlations equally. In this paper, we propose a smooth low-rank MVTC (SLR-MVTC) method, which aims to extract latent features that are smooth within each view and low-rank across views, enhancing clustering performance. Specifically, we first learn latent features from each view using orthogonal projection and then construct the latent feature tensor by concatenation and rotation. Then, we introduce a new smooth tensor nuclear norm to depict the low-rank components of the low-frequency parts in the feature tensor. Benefiting from the fast Fourier transform along the sample dimension, the obtained low-frequency components effectively capture local smoothness within views, while their low-rank parts further explore global correlations across views. Experimental results on six multi-view datasets demonstrate that SLR-MVTC outperforms state-of-the-art algorithms in terms of clustering performance and CPU time.