Improved Weighted Tensor Schatten <i>p</i> -Norm for Fast Multi-view Graph Clustering

Recently, tensor Schatten p-norm has achieved impressive performance for fast multi-view clustering [57]. This primarily ascribes the superiority of tensor Schatten p-norm in exploring high-order structure information among views. Whereas, 1) tensor Schatten p-norm treats different singular values equally, such that the larger singular values corresponding to certain significant feature information (i.e., prior information) have not been utilized fully; 2) tensor Schatten p-norm also ignore ranking the core entries of core tensor, which may contain noise information; 3) existing methods select fixed anchors or averagely update anchors to construct the neighbor bipartite graphs, greatly limiting the flexibility and expression of anchors. To break these limitations, we propose a novel Improved Weighted Tensor Schatten p-Norm for Fast Multi-view Graph Clustering (IWTSN-FMGC). Specifically, to eliminate the interference of the first two limitations, we propose an improved weighted tensor Schatten p-norm to dynamically rank core tensor and automatically shrink singular values. To this end, improved weighted tensor Schatten p-norm has the potential to more effectively leverage low-rank structures and prior information, thereby enhancing robustness compared to current tensor Schatten p-norm methods. Further, the designed adaptive neighbor bipartite graph learning can more flexibly and expressively encode the local manifold structure information than existing anchor selection and averaged anchor updating. Extensive experiments validate our effectiveness and superiority across multiple benchmark datasets.