High-order Complementarity Induced Fast Multi-View Clustering with Enhanced Tensor Rank Minimization

Recently, tensor-based multi-view clustering methods have achieved promising results, primarily benefited from their superior ability in exploring high-order consistent information among views. Despite significant progress, these methods inevitably suffer from several drawbacks: 1) Extremely high computational complexity restricts their feasibility for large-scale data sets. 2) Prevalently adopted tensor rank approximations (e.g., Tensor Nuclear Norm (TNN)) tend to under-penalize small singular values, resulting in noise residuals. 3) Tensor structure is rarely utilized for high-order complementarity investigation. In light of this, we propose High-order Complementarity Induced Fast Multi-View Clustering with Enhanced Tensor Rank Minimization (CFMVC-ETR). Specifically, two sets of representation matrices are learned from original multi-view data via the matrix factorization mechanism with a group of base matrices, which are further reconstructed into the consistent tensor and the complementary tensor, respectively. Subsequently, a novel Enhanced Tensor Rank is imposed on the consistent tensor, which is a tighter approximation of the tensor rank and is more noisy-robust to explore the high-order consistency. Meanwhile, a tensor-level constraint termed Tensorial Exclusive Regularization is proposed on the complementary tensor to enhance the view-specific feature and well capture the high-order complementarity. Moreover, we adopt a concatenation-fusion approach to integrate these two parts, deriving a discriminative unified embedding for the clustering task. We solve CFMVC-ETR by an efficient algorithm with good convergence. Extensive experiments on nine challenging data sets demonstrate the superiority of the proposed method.