Reliable Entropy-Induced Anchor Learning for Incomplete Multi-View Subspace Clustering

Under large-scale data with missing views, fast incomplete multi-view clustering (IMVC) with anchor learning is of critical importance due to its linear complexity $\mathcal {O}(n)$ . However, existing anchor-based methods only explore the column orthogonality of anchor points, where their arbitrary column orthogonal basis vectors have weak constraint relationships with real samples and significant deviations from more representative anchors, thereby impeding the precise representation of sample similarities. To solve this issue, we propose a Reliable Entropy-induced anchor learning for incomplete Multi-view subspace Clustering (REMC), which performs an entropy approximation term to learn more representative anchors, and we prove that the information entropy minimization can be relaxed into the $\ell _{2,1}$ -norm paradigm. Specifically, the proposed REMC first integrates anchor learning and subspace clustering to produce multiple view-specific bipartite graphs and capture the high-order correlations by imposing these bipartite graphs with the tensor nuclear norm. Then, we fuse all the view-specific bipartite graphs to build a consensus bipartite graph with entropy approximation regularization, and hence the proposed REMC can produce a more discriminative similarity graph, preserving each non-zero element in its column close to 1, while the other elements are approaching 0. Besides, an efficient algorithm is designed to solve the proposed REMC. Numerous results show the superior performance of our method on both the complete and incomplete data.