基于成对约束的不完整多视图聚类
Incomplete Multi-View Clustering with Pairwise Constraints
摘要: 不完整多视图聚类旨在处理样本在某些视图中缺失的聚类问题。 Incomplete multi-view spec- tral clustering with adaptive graph learning (IMSC AGL)是该领域的代表性方法,通过 联合图学习与谱聚类学习全局共识表示,并在多个数据集上表现良好。 然而,该方法仅对共识表 示施加正交约束,难以保证清晰的聚类结构和高判别性;同时,视图缺失时各视图聚类指示矩阵 中的噪声会干扰共识学习。 为此,本文在IMSC AGL框架上引入结构化成对约束顶,借助辅助变 量鼓励学习具有块对角结构的判别性共识表示,同时理论分析表明,该改进未增加额外高阶计算 负担。 在多个不完整多视图数据集上的实验表明,本文方法优于IMSC AGL及其他对比方法,验 证了改进的有效性。
Abstract: Incomplete multi-view clustering aims to handle clustering problems where samples are missing in some views. Incomplete multi-view spectral clustering with adaptive graph learning (IMSC AGL) is a representative method in this field, which learns a global consensus representation by jointly performing graph learning and spectral clus- tering, and performs well on multiple datasets. However, this method only imposes an orthogonal constraint on the consensus representation, making it difficult to ensure a clear clustering structure and high discriminability; moreover, when views are missing, noise in the cluster indicator matrices of individual views interferes with consensus learning. To this end, this paper introduces a structured pairwise constraint term in- to the IMSC AGL framework, encouraging the learning of a discriminative consensus representation with a block-diagonal structure via auxiliary variables, and theoretical analysis shows that this improvement does not incur additional high-order computa- tional burden. Experiments on multiple incomplete multi-view datasets demonstrate that the proposed method outperforms IMSC AGL and other comparison methods, verifying the effectiveness of the improvement.
文章引用:张婉怡, 唐科戚. 基于成对约束的不完整多视图聚类[J]. 应用数学进展, 2026, 15(10): 247-261. https://doi.org/10.12677/AAM.2026.1510412

参考文献

[1] Gao, Q., Li, F., Wang, Q., Gao, X. and Tao, D. (2025) Manifold Based Multi-View k-Means. IEEE Transactions on Pattern Analysis and Machine Intelligence, 47, 3175-3182. [Google Scholar] [CrossRef] [PubMed]
[2] Sadjadi, F., Jamshidi, M. and Asadi, A. (2025) Multi-View Clustering via Consensus Coeffi- cient Matrix and Separate Segmentation Matrices. Journal of Information and Telecommuni- cation, 9, 525-542. [Google Scholar] [CrossRef] 
[3] Zhang, X., Guo, X. and Pan, J. (2024) A New Nonconvex Multi-View Subspace Clustering via Learning a Clean Low-Rank Representation Tensor. Inverse Problems, 40, Article ID: 125007. [Google Scholar] [CrossRef] 
[4] Khalafaoui, Y., Matei, B., Lovisetto, M. and Grozavu, N. (2026) Deep Matrix Factoriza- tion with Adaptive Weights for Multi-View Clustering. Pattern Recognition, 170, Article ID: 112027. [Google Scholar] [CrossRef] 
[5] Liu, J., Liu, X., Zhang, Y., Zhang, P., Tu, W., Wang, S., et al. (2021). Self-Representation Subspace Clustering for Incomplete Multi-View Data. Proceedings of the 29th ACM Interna- tional Conference on Multimedia, 20-24 October 2021, 2726-2734.[CrossRef] 
[6] Wen, J., Zhang, Z., Zhang, Z., Fei, L. and Wang, M. (2021) Generalized Incomplete Multiview Clustering with Flexible Locality Structure Diffusion. IEEE Transactions on Cybernetics, 51, 101-114. [Google Scholar] [CrossRef] [PubMed]
[7] Wen, J., Zhang, Z., Xu, Y., Zhang, B., Fei, L. and Liu, H. (2019) Unified Embedding Alignment with Missing Views Inferring for Incomplete Multi-View Clustering. Proceedings of the AAAI Conference on Artificial Intelligence, 33, 5393-5400. [Google Scholar] [CrossRef] 
[8] Hu, M. and Chen, S. (2018) Doubly Aligned Incomplete Multi-View Clustering. Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, Stockholm, 13-19 July 2018, 2262-2268. [Google Scholar] [CrossRef] 
[9] Rai, N., Negi, S., Chaudhury, S. and Deshmukh, O. (2016) Partial Multi-View Clustering Using Graph Regularized NMF. 2016 23rd International Conference on Pattern Recognition (ICPR), Cancun, 4-8 December 2016, 2192-2197. [Google Scholar] [CrossRef] 
[10] Zhao, H., Liu, H. and Fu, Y. (2016) Incomplete Multi-Modal Visual Data Grouping. Twenty- Fifth International Joint Conference on Artificial Intelligence 2016, New York, 9-15 July 2016, 2392-23983.
[11] Wen, J., Xu, Y. and Liu, H. (2020) Incomplete Multiview Spectral Clustering with Adaptive Graph Learning. IEEE Transactions on Cybernetics, 50, 1418-1429. [Google Scholar] [CrossRef] [PubMed]
[12] Zhong, G. and Pun, C. (2023) Simultaneous Laplacian Embedding and Subspace Clustering for Incomplete Multi-View Data. Knowledge-Based Systems, 262, Article ID:110244. [Google Scholar] [CrossRef] 
[13] Gallier, J.H. (2013) Notes on Elementary Spectral Graph Theory. Applications to Graph Clus- tering Using Normalized Cuts. arXiv:1311.2492.
[14] Liang, J., Liu, X., Bai, L., Cao, F. and Wang, D. (2022) Incomplete Multi-View Clustering via Local and Global Co-Regularization. Science China Information Sciences, 65, Article No. 152105. [Google Scholar] [CrossRef] 
[15] Wang, Y., Li, A., Lu, G., Ding, W. and Zhou, H. (2025) Nonconvex Low-Rank Tensor Ap- proximation with Denoising Model for Multi-View Subspace Clustering. Applied Intelligence, 55, Article No. 1056. [Google Scholar] [CrossRef] 
[16] Wen, J., Han, N., Fang, X., Fei, L., Yan, K. and Zhan, S. (2019) Low-Rank Preserving Projection via Graph Regularized Reconstruction. IEEE Transactions on Cybernetics, 49, 1279-1291. [Google Scholar] [CrossRef] [PubMed]
[17] Wen, J., Fang, X., Cui, J., Fei, L., Yan, K., Chen, Y., et al. (2019) Robust Sparse Linear Discriminant Analysis. IEEE Transactions on Circuits and Systems for Video Technology, 29, 390-403. [Google Scholar] [CrossRef] 
[18] Shao, W., He, L. and Yu, P.S. (2015) Multiple Incomplete Views Clustering via Weighted Nonnegative Matrix Factorization with L2,1 Regularization. In: Appice, A., Rodrigues, P., Santos Costa, V., Soares, C., Gama, J. and Jorge, A., Eds., Machine Learning and Knowledge Discovery in Databases, Springer, 318-334. 20 [Google Scholar] [CrossRef] 
[19] Wang, H., Zong, L., Liu, B., Yang, Y. and Zhou, W. (2019) Spectral Perturbation Meets Incomplete Multi-View Data. Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, Macao, 10-16 August 2019, 3677-3683. [Google Scholar] [CrossRef] 
[20] Sokolova, M. and Lapalme, G. (2009) A Systematic Analysis of Performance Measures for Classification Tasks. Information Processing Management, 45, 427-437. [Google Scholar] [CrossRef]