Multi-view clustering (MVC) with bipartite graph has been extensively studied to rapidly handle multi-source heterogeneous information via sparse anchors. However, most existing methods follow a two-stage learning paradigm that first learns continuous label matrix and then discretizes it, not only bringing extra trade-off parameters but yielding suboptimal solutions. Also, numerous methods still exhibit limited scalability for large-scale problems. Thus, this paper proposes two novel models for discrete, trade-off parameter-free and rapid MVC. First, the Bipartite Graph Discrete Reconstruction (BGDR) model uniquely leverages the discrete label matrices of both samples and anchors to dynamically reconstruct a consensus bipartite graph across views. This concise reconstruction style eliminates redundant computations, and anchor labels enable to enrich cluster partition information during reconstruction, enhancing both accuracy and efficiency. The final clustering outcomes are directly acquired via discrete sample labels. Second, to free the optimization time overheads from the limitation of sample size, we further devise the Compact Graph Discrete Reconstruction (CGDR) model, which reconstructs a smaller compact affinity graph among anchors for significant acceleration. Original sample labels are then gained by label propagation. Systematic experiments illuminate that both models reach superior outcomes in term of efficacy and efficiency.

Multiview clustering aims to detect the consistent graph structure across each view, and has garnered extensive attention in recent years. However, the graph quality determines the clustering performance and cannot be updated in most methods, while the label extraction also relies on post-processing (e.g. spectral rotation). As a consequence, multiple objective functions are optimized independently, making it difficult to achieve one-pass clustering. Motivated by this, Graph-Free Multiview Clustering with Anchor (GMCA) is proposed towards coherence (in optimization), simplicity (in hyperparameters). Considering that similarity only exist among samples in the same cluster for ideal assignments, a label-based reverse framework is proposed for the first time to achieve feature approximation via graph-free factorization. Although non-negative label matrix exhibits indicative interpretability, cluster independence is overlooked, thus non-negative and orthogonal constraint is further imposed and proved beneficial for ideal graph backtracking. Besides, to prevent optimization from focusing on extreme approximating loss caused by redundant features, the Frobenius norm is employed, while allocating flexible view weights as collateral benefit. Comparison experiments with fourteen state-of-the-art methods are performed on eight real-world data sets, while our method exceeds the second-best method by up to$4.85\%$in clustering accuracy and keeps running time linear with samples number.

Recently, anchor-based strategy is getting a lot of attention, which extends spectral clustering to reveal the dual relation between samples and features. However, the acquisition of clustering results follows the relaxed-discrete procedure, which might lead to serious information loss. Given that, local-global fuzzy clustering with anchor graph is proposed in this article, which jointly completes subspace learning and clustering. With the construction of anchor graph, we first impose the fuzzy constraint on the indicator matrix, which is beneficial for revealing the ambiguity and uncertainty in clustering tasks. Thereafter, we introduce the graph divergence regularization term for maximizing the variance of fuzzy indicator matrix, which not only avoids the trivial solutions in local graph learning, but also enhances the separability of data for explicit global structure. In this way, the local graph loss and global divergence regularization term are able to jointly capture the critical clustering structure. Finally, we can obtain the clustering results in accordance with the optimal fuzzy indicator matrix, which is updated alternately by the presented coordinate descent method in optimization process. Therefore, the desirable discrete labels come out automatically under the fuzzy strategy without extra discretization operations, which conforms to reality. The effectiveness of our method will be demonstrated through comprehensive experimental results.