Incomplete multi-view clustering via efficient anchor tensor recovery framework

Tensor-based Incomplete Multi-view Clustering (TIMC) methods have received widespread attention due to the powerful data recovery capability of capturing cross-view high-order correlation. Although such methods have achieved remarkable progress, they still suffer from the following problems: (1) The extremely high computational complexity makes it hard for tensor-based methods to handle large-scale multi-view data. (2) Geometric structure constraints in the sample space often lead to high computational complexity and redundancy of structural information. (3) The commonly used Tensor Nuclear Norm (TNN) over-penalizes the primary rank components, leading to a sub-optimal representation tensor. Being aware of these, we propose Incomplete Multi-View Clustering with Efficient Anchor Tensor Recovery Framework (EATER). Specifically, it learns a group of anchors to construct a low-rank anchor tensor to recover the missing data with the high-order correlation among views and the geometric structure in the learned representation tensor is enhanced by an Anchor Laplacian Regularization (ALR). Moreover, instead of employing TNN, we adopt a tighter Non-convex Tensor Rank (NTR) to capture the multi-view high-order correlation effectively. An efficient iterative optimization algorithm is designed to solve the EATER, which is time-economical and enjoys favorable convergence. Extensive experimental results on various datasets demonstrate the superiority of the proposed algorithm as compared to state-of-the-art methods.