Anchors Crash Tensor: Efficient and Scalable Tensorial Multi-View Subspace Clustering

Tensorial Multi-view Clustering (TMC), a prominent approach in multi-view clustering, leverages low-rank tensor learning to capture high-order correlation among views for consistent clustering structure identification. Despite its promising performance, the TMC algorithms face three key challenges: 1). The severe computational burden makes it difficult for TMC methods to handle large-scale datasets. 2). Estimation bias problem caused by the convex surrogate of the tensor rank. 3). Lack of explicit balance of consistency and complementarity. Being aware of these, we propose a basic framework Efficient and Scalable Tensorial Multi-View Subspace Clustering (ESTMC) for large-scale multi-view clustering. ESTMC integrates anchor representation learning and non-convex function-based low-rank tensor learning with a Generalized Non-convex Tensor Rank (GNTR) into a unified objective function, which enhances the efficiency of the existing subspace-based TMC framework. Furthermore, a novel model ESTMC-C$^{2}$ with the proposed Enhanced Tensor Rank (ETR), Consistent Geometric Regularization (CGR), and Tensorial Exclusive Regularization (TER) is extended to balance the learning of consistency and complementarity among views, delivering divisible representations for the clustering task. Efficient iterative optimization algorithms are designed to solve the proposed ESTMC and ESTMC-C$^{2}$, which enjoy time-economical complexity and exhibit theoretical convergence. Extensive experimental results on various datasets demonstrate the superiority of the proposed algorithms as compared to state-of-the-art methods.