Abstract: Anchor-based bipartite graphs can approximate sample relationships with low computational cost, and have been widely used for graph construction in large-scale multi-view clustering. However, most existing methods generate anchors by random sampling, K-Means centers, or static dictionaries. The anchor positions are usually fixed before graph learning. For data with non-spherical clusters, ring-shaped clusters, elongated clusters, and large density differences among clusters, static anchors are difficult to approach local density peaks and curved cluster boundaries. This may lead to anchor mismatch. The sample-anchor bipartite graph constructed in this way may contain redundant or unreliable connections, which affects cross-view structure fusion and reduces the stability of clustering results. To address these problems, a Multi-view Bipartite Graph Clustering method guided by Mean-Shift (MBGC-MS) is proposed. The aim of the method is to maintain the high efficiency of anchor graphs, improve the adaptive representation ability of anchors for complex data distributions, and integrate graph learning and clustering assignment into a unified optimization process. First, an anchor set is initialized in each view. Mean Shift is then used to iteratively update the anchors along the kernel density gradient, so that the anchors are changed from Euclidean center representatives to local density modes. After that, the local bandwidth is estimated according to the distance from each sample to its neighboring anchors. Only the neighboring anchor relationships of each sample are retained to construct a sparse and density-aware sample-anchor bipartite graph. Second, the bipartite graph of each view is decomposed into a shared consistency graph and view-specific complementary graphs. The consistency graph is used to describe the clustering structure jointly supported by different views, and a nuclear norm constraint is imposed to enhance its low-rank property and structural compactness. The complementary graph is used to preserve the discriminative local information that deviates from the consensus in each single view, and a sparsity constraint is imposed to suppress noise and redundant connections. Third, view weights are adaptively learned according to the reconstruction error, so as to avoid the information interference caused by equal-weight fusion of all views. On this basis, the consistency graph and complementary graphs are fused to construct a unified sample-anchor bipartite graph and an augmented Laplacian matrix. A spectral trace constraint is further imposed to make the unified graph tend to form a given number of connected components. The proposed model adopts a block coordinate descent strategy to alternately update the clustering indicator matrix, consistency graph, complementary graphs, and view weights. Each subproblem can be solved by eigen-decomposition, soft-thresholding operator, singular value thresholding, or quadratic programming. In this way, one-step optimization of graph structure learning and clustering assignment is achieved. Experiments are conducted on four multi-view datasets, including Handwritten, BBC-sport, MSRC_v1, and Caltech101-7. ACC, NMI, and F-score are used as evaluation metrics. The results show that the proposed method obtains the best performance on 8 out of 12 metrics. On Handwritten, the highest NMI is obtained, reaching 0.949. On BBC-sport, the ACC and F-score reach 0.971 and 0.933, respectively. On MSRC_v1, the ACC and F-score reach 0.966 and 0.931, respectively. On Caltech101-7, the ACC, NMI, and F-score reach 0.711, 0.521, and 0.484, respectively, and all three metrics are the best. Ablation experiments further show that Mean Shift anchor updating, consistency-complementarity decomposition, and Laplacian spectral trace constraint all contribute to performance improvement. On Caltech101-7, the ACC, NMI, and F-score of the complete model are higher than those of the model using only the Mean Shift module, whose corresponding values are 0.534, 0.362, and 0.348. The comparison of different anchor strategies shows that the three metrics of Mean Shift anchors are 0.711, 0.521, and 0.484, which are clearly higher than those of K-Means anchors, namely 0.576, 0.395, and 0.456, and also higher than those of random sampling anchors, namely 0.308, 0.260, and 0.320. The convergence experiments show that the objective function usually decreases rapidly in the first 5–10 iterations and becomes stable within 20 iterations. Complexity analysis and running time experiments show that, when the number of anchors and iterations are fixed, the running time of the algorithm grows approximately linearly with the sample size. In summary, the proposed method can calibrate anchor positions by using density information and enhance the representation ability of bipartite graphs for complex cluster structures. It also considers multi-view consistency, complementarity, and one-step clustering optimization. Therefore, it shows good clustering performance, stability, and scalability on non-spherical and uneven-density data.

摘要： 锚点二分图能够以较低计算代价近似样本间关系，是大规模多视图聚类中的常用图构建方式。但现有方法多采用随机采样、K-Means中心或静态字典生成锚点，锚点位置通常在图学习前固定。在非球形簇、环状簇、长条状簇以及簇间密度差异较大的数据中，静态锚点难以贴近局部密度峰与弯曲簇边界，容易产生锚点失配。由此构造的样本–锚点二分图会包含冗余连接或不可靠连接，影响跨视图结构融合，并降低聚类结果的稳定性。针对上述问题，提出一种均值漂移引导的多视图锚点二分图聚类方法。该方法的目标是在保持锚点图高效率的同时，提高锚点对复杂数据分布的自适应刻画能力，并将图学习与聚类划分纳入统一优化过程。首先，在每个视图中初始化锚点集合，并利用Mean Shift沿核密度梯度迭代更新锚点，使锚点由欧氏中心代表点转向局部密度模式。随后，根据样本到近邻锚点的距离估计局部带宽，只保留每个样本的近邻锚点关系，构造稀疏且密度感知的样本–锚点二分图。其次，将各视图二分图分解为共享一致性图和视图特有互补图。一致性图用于刻画不同视图共同支持的聚类结构，并施加核范数约束以增强低秩性和结构紧致性；互补图用于保留单个视图中偏离共识但具有判别作用的局部信息，并施加稀疏约束以抑制噪声和冗余连接。再次，依据重构误差自适应学习视图权重，避免各视图等权融合带来的信息干扰。在此基础上，融合一致性图与互补图，构造联合样本–锚点二分图和增广拉普拉斯矩阵，并通过谱迹约束使联合图趋向于形成给定数量的连通分量。模型采用块坐标下降策略交替更新聚类指示矩阵、一致性图、互补图和视图权重。各子问题可通过特征分解、软阈值算子、奇异值阈值和二次规划求解，从而实现图结构学习与聚类划分的一步优化。实验在Handwritten、BBC-sport、MSRC_v1和Caltech101-7四个多视图数据集上进行，并采用ACC、NMI和F-score评价性能。结果表明，所提方法在12项指标中获得8项最优。在Handwritten上取得最高NMI，为0.949；在BBC-sport上ACC和F-score分别达到0.971和0.933；在MSRC_v1上ACC和F-score分别达到0.966和0.931；在Caltech101-7上ACC、NMI和F-score分别达到0.711、0.521和0.484，三项指标均为最优。消融实验进一步表明，Mean Shift锚点更新、一致性–互补性分解和拉普拉斯谱迹约束均对性能提升有贡献。在Caltech101-7上，完整模型的ACC、NMI和F-score高于仅使用Mean Shift模块的0.534、0.362和0.348。不同锚点策略对比显示，Mean Shift锚点的三项指标为0.711、0.521和0.484，明显高于K-Means锚点的0.576、0.395和0.456，也高于随机采样锚点的0.308、0.260和0.320。收敛性实验显示，目标函数通常在前5–10次迭代内快速下降，并在20次迭代内趋于稳定。复杂度分析与运行时间实验表明，在固定锚点数和迭代次数时，算法运行时间随样本规模近似线性增长。综上，所提方法能够利用密度信息校准锚点位置，增强二分图对复杂簇结构的表达能力，同时兼顾多视图一致性、互补性与一步聚类优化，在非球形和密度不均数据上表现出较好的聚类效果、稳定性和可扩展性。