Abstract: Multi-view subspace clustering aims to learn latent shared structures by exploiting the consistency, complementarity, and discrepancy information among multiple feature sources. How to simultaneously preserve global structural relationships, local geometric characteristics, and representation stability during feature fusion remains a critical issue in this field. Existing methods are mainly built upon low-rank representation, sparse constraints, or graph learning mechanisms. Although they can exploit cross-view shared information to some extent, they still lack sufficient collaborative modeling of global structure preservation, local smoothness constraints, and robust representation learning, making them prone to local structure distortion, unstable representations, and degraded clustering performance under noise contamination, outlier perturbations, and complex data distributions. To address these issues, this paper proposes a Structured Local Smooth Multi-View Subspace Clustering (SLS-MVSC) method. Under a unified self-representation learning framework, the proposed method jointly incorporates low-rank constraints, Total Variation (TV) regularization, graph regularization, and robust error modeling to achieve collaborative optimization of global information learning, local relationship preservation, and stable representation learning. Specifically, low-rank constraints are employed to learn shared representations across multiple views, thereby capturing the latent consistent global subspace structure among different views and enhancing the modeling capability for cross-view common information. Considering that noise interference may cause severe fluctuations in the self-representation matrix, TV regularization is introduced into the self-representation learning process to preserve representation continuity and boundary structures by restricting abrupt local variations, thereby improving the smoothness and stability of learned representations. Furthermore, graph regularization is adopted to maintain neighborhood relationship consistency among samples. By explicitly modeling local manifold structures, the proposed method strengthens the characterization of data geometric relationships and enables the learned representations to better conform to the intrinsic distribution characteristics of the original data. Meanwhile, a robust norm is introduced into the reconstruction error term to enhance the model’s adaptability to outliers and complex noise, thereby improving representation quality and clustering robustness from multiple perspectives. To optimize the proposed model, an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM) is developed. By introducing auxiliary variables, the complex objective function is decomposed into several independently solvable subproblems, and the update rules for all variables together with the overall optimization procedure are derived, ensuring training stability and computational efficiency. Extensive experiments are conducted on six publicly available datasets to evaluate the effectiveness of the proposed method and compare it with several representative multi-view clustering approaches. Experimental results demonstrate that the proposed method achieves superior performance in terms of Clustering Accuracy (ACC), Normalized Mutual Information (NMI), Purity (PUR), Adjusted Rand Index (AR), and F-score, attaining optimal or near-optimal results on multiple datasets and exhibiting strong clustering capability and cross-dataset adaptability. Further ablation studies verify the positive contribution of each module to performance improvement. Among them, low-rank constraints and graph regularization play important roles in global structure learning and local geometric relationship preservation, respectively, while TV regularization is particularly effective in enhancing representation smoothness, alleviating noise-induced representation fluctuations, and improving model stability. Robustness experiments further demonstrate that the proposed method maintains stable performance under different noise intensities, indicating its effectiveness in mitigating the adverse influence of noise on feature representation learning and clustering results. In summary, the proposed SLS-MVSC method effectively improves clustering performance, representation stability, and noise robustness, providing an effective solution for complex multi-view data clustering tasks.

摘要： 多视图子空间聚类旨在利用多源特征间的一致性、互补性与差异性信息学习潜在共享结构。如何在特征融合过程中兼顾全局结构关系、局部几何特征与表示稳定性，是该领域的重要问题。现有方法多基于低秩表示、稀疏约束或图学习机制构建统一模型，虽然能够在一定程度上挖掘跨视图共享信息，但对全局结构保持、局部平滑约束与鲁棒表示学习之间的协同建模仍不充分，导致模型在噪声污染、异常扰动及复杂分布条件下易出现局部结构失真、表示不稳定及聚类性能退化问题。针对上述问题，本文提出一种面向结构保持的局部平滑多视图子空间聚类方法（SLS-MVSC）。所提方法在统一自表示学习框架下联合引入低秩约束、全变差（TV）范数约束、图正则化约束以及鲁棒误差建模机制，实现全局信息学习、局部关系保持与稳定表示优化的协同建模。首先，利用低秩约束学习多视图共享表示，以挖掘不同视图间潜在一致的全局子空间结构，增强模型对跨视图公共信息的表达能力。其次，考虑噪声干扰容易导致自表示矩阵产生剧烈波动，本文在自表示学习过程中引入TV范数约束，通过限制局部区域表示变化幅度保持表示连续性与边界结构，从而提高表示结果的平滑性与稳定性。进一步地，引入图正则化约束保持样本间邻域关系一致性，通过显式建模局部流形结构增强模型对数据几何关系的刻画能力，使学习得到的表示更加符合原始数据的内在分布特征。同时，在重构误差项中采用鲁棒范数增强模型对异常样本与复杂噪声的适应能力，从多个层面提升表示质量与聚类鲁棒性。针对所构建的优化模型，本文设计基于交替方向乘子法（ADMM）的迭代求解算法，通过引入辅助变量对复杂目标函数进行分解优化，将原问题转化为多个可独立求解的子问题，并推导得到各变量的更新过程与整体求解流程，从而保证模型训练过程的稳定性与求解效率。为了验证所提方法的有效性，本文在6个公开数据集上开展实验研究，并与多种代表性多视图聚类方法进行对比。实验结果表明，所提方法在聚类准确率（ACC）、归一化互信息（NMI）、纯度（PUR）、调整兰德指数（AR）及F-score等指标上均取得优异性能，在多个数据集上达到最优或接近最优结果，展现出良好的聚类性能与跨数据集适应能力。进一步的消融实验验证了各组成模块对模型性能提升的积极作用，其中低秩约束和图正则化分别在全局结构学习与局部几何关系保持方面发挥重要作用，而TV范数约束在增强表示平滑性、缓解噪声引起的表示震荡以及提高模型稳定性方面表现尤为突出。鲁棒性实验结果进一步表明，在不同强度噪声条件下，所提方法整体仍能够保持稳定性能，说明模型能够有效减弱噪声扰动对特征表示学习与聚类结果的影响。综上所述，所提SLS-MVSC方法能够有效提升多视图数据的聚类性能、表示稳定性与抗噪能力，为复杂多视图数据分析提供了一种有效的子空间聚类方法。