Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering

In the context of multi-view clustering, graph learning is recognized as a crucial technique, which generally involves constructing an adaptive neighbor graph based on probabilistic neighbors, and then learning a consensus graph to for clustering. However, they are confronted with two limitations. Firstly, they often rely on Euclidean distance to measure similarity when constructing the adaptive neighbor graph, which proves inadequate in capturing the intrinsic structure among data points in practice. Secondly, most of these methods focus solely on consensus graph, ignoring unique information from each view. Although a few graph-based studies have considered using specific information as well, the modelling approach employed does not exclude the noise impact from the specific component. To this end, we propose a novel tensor-based multi-view graph learning framework that simultaneously considers consistency and specificity, while effectively eliminating the influence of noise. Specifically, we calculate similarity distance on the Stiefel manifold to preserve the intrinsic properties of data. By making an assumption that the learned neighbor graph of each view comprises a consistent part, a specific part, and a noise part, we formulate a new tensor-based target graph learning paradigm for noise-free graph fusion. Owing to the benefits of tensor singular value decomposition (t-SVD) in uncovering high-order correlations, this model is capable of achieving a complete understanding of the target graph. Furthermore, we derive an algorithm to address the optimization problem. Experiments on six datasets have demonstrated the superiority of our method. We have released the source code on https://github.com/lshi91/CSTGL-Code.