Incomplete Multi-View Clustering based on Semi-Definite Constraint and Tensor Low-Rank Learning

Zizheng Yuan

doi:10.63313/JCSFT.9039

Authors

Zizheng Yuan School of Computer Science and Technology, Qingdao University, Qingdao 266071, China Author

DOI:

https://doi.org/10.63313/JCSFT.9039

Keywords:

Incomplete views, Tensor Low-Rank Learning, Semi-Definite Constraint

Abstract

Incomplete Multi-View Clustering (IMVC) faces significant challenges in preserving high-order correlations and the Positive Semi-Definite (PSD) property of missing kernels. This paper proposes a novel approach, a unified framework that simultaneously performs kernel completion and consensus graph learning. The method leverages tensor low-rank constraints to capture global consistency across views and explicitly enforces a strict PSD constraint to ensure kernel validity. An efficient Augmented Lagrangian Multiplier (ALM)-based algorithm is developed to solve the optimization problem. Experimental results demonstrate the superiority of the method over state-of-the-art methods.

References

[1] Chao G, Sun S, Bi J. (2021) A survey on multiview clustering. IEEE Transactions on Artificial Intelligence, 2, 146–168. https://doi.org/10.1109/TAI.2021.3065894

[2] Gönen M, Margolin AA. (2014) Localized data fusion for kernel k-means clustering with application to cancer biology. In: Proceedings of the 28th International Conference on Neural Information Processing Systems (NIPS 2014), 1305–1313.

[3] Liang W, Liu J, Zhang Y, Wang S. (2022) Multi-view spectral clustering with high-order optimal neighborhood Laplacian matrix. IEEE Transactions on Knowledge and Data Engineering, 34, 3418–3430. https://doi.org/10.1109/TKDE.2020.3025100

[4] Wang S, Tao Z, Liu H, Yang Y. (2022) Highly-efficient incomplete largescale multiview clustering with consensus bipartite graph. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 9766–9775.

[5] Menglei, Hu & Chen, Songcan. (2018). Doubly Aligned Incomplete Multi-view Clustering. 2262-2268. 10.24963/ijcai.2018/313.

[6] Zhang, Changqing & Fu, Huazhu & Liu, Si & Liu, Guangcan & Cao, Xiaochun. (2015). Low-Rank Tensor Constrained Multiview Subspace Clustering. 10.1109/ICCV.2015.185.

[7] Shao W, He L, Yu PS. (2015) Multiple incomplete views clustering via weighted nonnegative matrix factorization with L2,1 regularization. In: Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), 318–334. https://doi.org/10.1007/978-3-319-23528-8_20

[8] Qiyue Yin, Shu Wu, and Liang Wang. 2015. Incomplete Multi-view Clustering via Subspace Learning. In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management (CIKM '15). Association for Computing Machinery, New York, NY, USA, 383–392. https://doi.org/10.1145/2806416.2806526

[9] Derek Greene and Pádraig Cunningham. 2006. Practical solutions to the problem of diagonal dominance in kernel document clustering. In Proceedings of the 23rd international conference on Machine learning (ICML '06). Association for Computing Machinery, New York, NY, USA, 377–384. https://doi.org/10.1145/1143844.1143892

[10] Yang M, Li Y, Huang Z, Liu Z, Hu P, Peng X. (2021) Partially view-aligned representation learning with noise-robust contrastive loss. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 1134–1143. https://doi.org/10.1109/CVPR46437.2021.00119

[11] Ng, A., Michael I. Jordan and Yair Weiss. “On Spectral Clustering: Analysis and an algorithm.” Neural Information Processing Systems (2001).

[12] Handong Zhao, Hongfu Liu, and Yun Fu. 2016. Incomplete multi-modal visual data grouping. In Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI'16). AAAI Press, 2392–2398.

[13] Hu, Menglei and Songcan Chen. “One-Pass Incomplete Multi-view Clustering.” AAAI Conference on Artificial Intelligence (2019).

[14] J. Wen, Y. Xu and H. Liu, "Incomplete Multiview Spectral Clustering With Adaptive Graph Learning," in IEEE Transactions on Cybernetics, vol. 50, no. 4, pp. 1418-1429, April 2020, doi: 10.1109/TCYB.2018.2884715.

[15] Wang, Hao, Linlin Zong, Bing Liu, Yan Yang, and Wei Zhou. 2019. “Spectral Perturbation Meets Incomplete Multi-View Data.” In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence. doi:10.24963/ijcai.2019/510.

[16] Xiao Cai, Feiping Nie, and Heng Huang. 2013. Multi-view K-means clustering on big data. In Proceedings of the Twenty-Third international joint conference on Artificial Intelligence (IJCAI '13). AAAI Press, 2598–2604.

[17] Liu X, Zhu X, Li M, et al. Multiple Kernel k-Means with Incomplete Kernels. IEEE Trans Pattern Anal Mach Intell. 2020;42(5):1191-1204. doi:10.1109/TPAMI.2019.2892416.

[18] Lin Z, Chen M, Ma Y. (2010) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv preprint arXiv:1009.5055. https://arxiv.org/abs/1009.5055

[19] Misha E. Kilmer, Karen Braman, Ning Hao, and Randy C. Hoover. 2013. Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging. SIAM J. Matrix Anal. Appl. 34, 1 (2013), 148–172. https://doi.org/10.1137/110837711

[20] S. Zhou et al., "Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation," in IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 4, pp. 1351-1362, April 2020, doi: 10.1109/TNNLS.2019.2919900.

[21] Schafer JL, Graham JW. Missing data: our view of the state of the art. Psychol Methods. 2002;7(2):147-177.

[22] L. Li et al., "Local Sample-Weighted Multiple Kernel Clustering With Consensus Discriminative Graph," in IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 2, pp. 1721-1734, Feb. 2024, doi: 10.1109/TNNLS.2022.3184970.

[23] Peng C, Liu C, Bai Y, Chen Y, Kang Z, Dong J, et al. Fine-grained tensor completion for incomplete multi-view clustering. Pattern Recognit. 2026;174:112956. doi:10.1016/j.patcog.2025.112956.