Topology-Driven Multi-View Clustering via Tensorial Refined Sigmoid Rank Minimization

Benefiting from the effective exploitation of the high-order correlations across multiple views, tensor-based multi-view clustering (TMVC) has garnered considerable attention in recent years. Nevertheless, prior TMVC techniques commonly involve assembling multiple view-specific spatial similarity graphs into a three-dimensional tensor, overlooking the intrinsic topological structure essential for precise clustering of data within a manifold. Additionally, mainstream techniques are constrained by equally shrinking all singular values to recover a low-rank tensor, limiting their capacity to distinguish significant variations among different singular values. In this investigation, we present an innovative TMVC framework termed toPology-driven multi-view clustering viA refined teNsorial sigmoiD rAnk minimization (PANDA ). Specifically, PANDA extracts view-specific topological structures from Euclidean graphs and intricately integrates them into a low-rank three-dimensional tensor, facilitating the concurrent utilization of intra-view topological connectivity and inter-view high-order correlations. Moreover, we develop a refined sigmoid function as the tighter surrogate to tensor rank, enabling the exploration of significant information of heterogeneous singular values. Meanwhile, the topological structures are merged into a unified structure with varying weights, associated with a connectivity constraint, empowering the significant divergence among views and the explicit cluster structure of the target graph are simultaneously leveraged. Extensive experiments demonstrate the superiority of PANDA, outperforming SOTA methods.