Although previous graph-based multi-view clustering algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k-means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this paper presents an efficient multi-view clustering approach via unified and discrete bipartite graph learning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Further, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

翻译：虽然以往的基于图的多视图聚类算法取得了显著进展，但大多数仍面临三个局限性。首先，它们通常具有较高的计算复杂度，限制了在大规模场景中的应用。其次，它们通常仅在单视图层面或视图共识层面进行图学习，但往往忽略了单视图图与共识图联合学习的可能性。第三，许多方法依赖k-means对谱嵌入进行离散化处理，缺乏直接学习具有离散聚类结构的图的能力。针对这一问题，本文提出了一种基于统一离散二分图学习的高效多视图聚类方法（UDBGL）。具体而言，引入锚点引导的子空间学习从多个视图中学习视图特定的二分图，在此基础上利用二分图融合策略通过自适应权重学习获得视图共识二分图。进一步施加拉普拉斯秩约束，确保融合后的二分图具有离散聚类结构（即特定数量的连通分量）。通过将视图特定二分图学习、视图共识二分图学习以及离散聚类结构学习统一建模为单一目标函数，本文设计了一种高效的优化算法来解决该问题，并直接获得离散聚类结果而无需额外划分，值得注意的是其时间复杂度与数据规模呈线性关系。在多个多视图数据集上的实验证明了UDBGL方法的鲁棒性和高效性。代码已开源在https://github.com/huangdonghere/UDBGL。