Embedded Multi-view Clustering via Fusing Tensor Subspace Representation and Adaptive Graph Learning

Multi-view clustering (MVC) aims to uncover the consistent structure and latent distribution of data by integrating information from diverse perspectives. A series of MVC models have been developed, but most of them are limited. They either naively fuse multi-view data into a single view or process each view in isolation, thereby neglecting the complex relationships between views. Among which, multi-stage approaches are heavily dependent on pre-learning and post-processing steps. To overcome these limitations, a one-stage MVC model, namely the embedded multi-view clustering approach with tensor self-representation and adaptive graph learning (EMCTGL), is proposed. In the proposed model, a step-structured data tensor is constructed and then decomposed to learn a cross-view self-representation tensor, effectively capturing the global topological relationships across all views. To achieve a clearer global subspace structure, a novel TLog-induced non-convex low-rank regularization is imposed on the rotated representation tensor. Under relaxed symmetry constraints, the self-representative tensor guides the learning of view-specific affinity graphs and a σ-norm penalty is applied to promote approximation of symmetry of affinity graphs. Subsequently, the normalized view-specific graphs are adaptively fused and factorized into the final clustering indicator matrix by embedding the semi-non-negative decomposition within a one-stage framework. To reduce the computational complexity, EMCTGL is extended to an anchor-driven MVC through determining anchors based on an adaptive density-peak strategy. Effective optimization schemes are devised to solve these non-convex models. Extensive experiments on various real-world datasets demonstrate that EMCTGL outperforms current state-of-the-art techniques.