Multi-view subspace clustering (MSC) is widely studied owing to the ability to capture the diverse and complementary information hidden in multiple views. As a representative model, tensorial MSC can capture global information by leveraging high-order correlations across various perspectives, leading to promising results. However, this approach fails to reveal the local structure in the specific view and ignores the prior information of the self-representation tensor. To address the problems, we propose the novel graph-guided local structure propagation (GGLSP) for tensorial MSC. First, we improve the adaptive graph model to acquire a fused graph similarity matrix for extracting the relationships between samples and propagating the local structure information to the self-representation tensor. Subsequently, we introduce the weighted tensor Schatten p-norm to approximate the tensor rank function by exploiting the contributions of different singular values so that the self-representation tensor can better reveal the global low-rank structure information. Finally, we develop two efficient algorithms to solve the optimization problems. Large numbers of experiments on seven popular datasets confirm the superiority of our proposed GGLSP.
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