Tensorial Multi-View Clustering via Alternative Rank Minimization and Inter-View Alignment

Tensor-based multi-view clustering is a popular approach. It can enhance representation learning by exploring higher-order correlations among views. However, two key issues remain unsolved. First, minimizing the tensor rank is a complex multi-objective optimization problem, so finding a suitable optimization strategy is an open problem. Moreover, most tensor methods require two phases to obtain the consensus matrix, which usually leads to suboptimal performance. To address these issues, we propose a Tensorial Multi-view Clustering via Alternative Rank Minimization and Inter-view Alignment (ARIA), in which multiple low-rank matrices and the consistent matrix are jointly optimized in a unified framework. Specifically, we stack the representations obtained from different views into a higher-order tensor. Then, a non-convex alternative rank-minimizing regularization is introduced to achieve a tighter approximation of the rank function. Besides, we impose intra-view alignment constraints to establish a connection between inter-view and intra-view. Unlike the previous method, it is a one-step strategy to obtain the consensus representation. Notably, our approach requires only linear complexity, and thus it can be successfully applied in large-scale clustering tasks. Extensive experiments validate the effectiveness and scalability of the proposed method. The code for ARIA is publicly available athttps://github.com/zskong/ARIA.