Auto-weighted Tensor Schatten p-Norm for Robust Multi-view Graph Clustering

Abstract

Recently, tensor-singular value decomposition based tensor-nuclear norm (t-TNN) has achieved impressive performance for multi-view graph clustering. This primarily ascribes the superiority of t-TNN in exploring high-order structure information among views. However, 1) t-TNN cannot ideally approximate to the original rank minimization, which produces the suboptimal graph tensor; in addition, t-TNN treats different singular values equally, such that the larger singular values corresponding to certain significant feature information (i.e., prior information) has not been utilized fully; 2) the data of original high-dimensional space are often corrupted by noise and outliers, which always makes adaptive neighbors graph learning (ANGL) generate low-quality affinity graphs. To address these issues, we propose a novel multi-view graph clustering method termed auto-weighted tensor Schatten p-norm (t-ATSN) for robust multi-view graph clustering (t-ATSN-RMGC). Concretely, we first propose t-SVD based t-ATSN with 0<p<1 to make the learned graph tensor better approximate the target rank than t-TNN. Meanwhile, it can also automatically and appropriately shrink singular values for constructing a more refined graph tensor, so as to fully capture spatial structure in the graph tensor. Moreover, we introduce the Geman McClure loss function to enhance the robustness of ANGL for noise and outliers. Experimental results on benchmarks across different scenarios and sizes show that the proposed method consistently outperforms state-of-the-art methods.