Low-Rank Tensor Representation Learning for Multi-View Clustering

doi:10.3778/j.issn.1002-8331.2106-0157

Abstract

Abstract: Aiming at the problem that the existing robust graph learning ignores the complementary information and high-order correlation between multiple views, a low-rank tensor representation learning for multi-view clustering（LRTRL-MVC） is proposed. Firstly, using the idea of robust principal component analysis, the robust graph and transition probability matrix of each view are calculated on the clean data with noise removed, and then a tensor containing the Markov transition probability matrix of each view is constructed. Finally, the nuclear norm based on tensor singular value decomposition is used to ensure the low rank property of the target tensor. The low rank tensor is used as the input of Markov spectral clustering algorithm to obtain the final clustering result. Experiments are carried out on four different types of public standard datasets BBCSport, NGs, Yale and MSRCv1, and compared with the related best multi view clustering algorithm. The results show that the clustering results of the proposed algorithm are higher than other comparison algorithms under the three clustering metrics.

Key words: multi-view clustering, Markov chain, low-rank tensor

摘要： 针对现有鲁棒图学习忽略多视图间的互补信息和高阶相关性问题，提出一种面向多视图聚类的低秩张量表示学习（LRTRL-MVC）算法。利用鲁棒主成分分析的思想，在去除噪声的干净数据上计算各视图的鲁棒图和转移概率矩阵，然后构建一个包含各视图马尔可夫转移概率矩阵的张量，采用基于张量奇异值分解的核范数来确保目标张量的低秩性质。利用迭代最优化算法求解，将求得的低秩张量作为马尔可夫谱聚类算法的输入得到最终聚类结果。在4个不同类型的公开标准数据集BBCSport、NGs、Yale和MSRCv1上进行实验并与相关的最好多视图聚类算法进行对比，结果表明在3个聚类度量标准下，所提算法的聚类结果均高于其他对比算法。

关键词: 多视图聚类, 马尔可夫链, 低秩张量

YU Yao, DU Shiqiang, SONG Jinmei. Low-Rank Tensor Representation Learning for Multi-View Clustering[J]. Computer Engineering and Applications, 2022, 58(13): 154-163.

余瑶, 杜世强, 宋金梅. 面向多视图聚类的低秩张量表示学习[J]. 计算机工程与应用, 2022, 58(13): 154-163.

References

[1] MACQUEEN J B.Some methods for classification and analysis of multivariate observations[C]//Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability，1967：281-297.
[2] NG A Y，JORDAN M I，WEISS Y，et al.On spectral clustering：Analysis and an algorithm[C]//Advances in Neural Information Processing Systems，2002：849-856.
[3] 胡文涛，陈秀宏.基于局部保持投影的鲁棒稀疏子空间学习[J].计算机工程与应用，2021，57（10）：194-199.
HU W T，CHEN X H.Robust sparse subspace learning based on locality preserving projections[J].Computer Engineering and Applications，2021，57（10）：194-199.
[4] WANG Y X，XU H，LENG C，et al.Provable subspace clustering：When LRR meets SSC[J].IEEE Transactions on Information Theory，2019，65（9）：5406-5432.
[5] LIU G C，LIN Z C，YAN S C，et al.Robust recovery of subspace structures by low-rank representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence，2013，35（1）：171-184.
[6] ELHAMIFAR E，VIDAL R.Sparse subspace clustering：Algorithm，theory，and applications[J].IEEE Transactions on Pattern Analysis and Machine Intelligence，2013，35（11）：2765-2781.
[7] Li C G，VIDAL R.Structured sparse subspace clustering：A unified optimization framework[C]//Proceedings of IEEE Conference on Computer Vision and Pattern Recognition，2015：277-286.
[8] KANG Z，PAN H，XU Z L，et al.Robust graph learning from noisy dataC]//Proceedings of IEEE Conference on IEEE Transactions on Cybernetics，2020，50（5）：1833-1843.
[9] GAO H C，NIE F P，LI X L，et al.Multi-view subspace clustering[C]//Proceedings of IEEE International Conference on Computer Vision，2016：4238-4246.
[10] WANG X B，GUO X J，ZHEN L，et al.Exclusivity-consistency regularized multi-view subspace clustering[C]//Proceedings of IEEE Conference on Computer Vision and Pattern Recognition，2017：1-9.
[11] BRBIC M，KOPRIVA I.Multi-view low-rank sparse subspace clustering[J].Pattern Recognition，2017，73：247-258.
[12] LIN S X，ZHONG G，SHU T.Simultaneously learning feature-wise weights and local structures for multi-view subspace clustering[J].Knowledge-Based Systems，2020，205：106280.
[13] NIE F P，WANG X Q，JORDAN M I，et al.The constrained Laplacian rank algorithm for graph-based clustering[M].[S.l.]：AAAI Press，2016：1969-1976.
[14] NIE F P，CAI G H，LI X L.Multi-view clustering and semi-supervised classification with adaptive neighbours[C]//Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence，2017：2408-2414.
[15] NIE F P，WU D Y，WANG R，et al.Self-weighted clustering with adaptive neighbors[J].IEEE Transactions on Neural Networks and Learning Systems，2020，31（9）：3428-3441.
[16] XIA R K，PAN Y，DU L，et al.Robust multi-view spectral clustering via low-rank and sparse decomposition[C]//Proceedings of the 28th AAAI Conference on Artificial Intelligence，2014：2149-2155.
[17] ZHANG C Q，HU Q H，FU H Z，et al.Latent multi-view subspace clustering[C]//Proceedings of IEEE Conference on Computer Vision and Pattern Recognition，2017：4333-4341.
[18] XIE Y，TAO D C，ZHANG W S，et al.On unifying multiview self-representations for clustering by tensor multi-rank minimization[J].International Journal of Computer Vision，2018，126（11）：1157-1179.
[19] GAO Q X，XIA W，WAN Z Z，et al.Tensor-SVD based graph learning for multi-view subspace clustering[C]//Proceedings of the AAAI Conference on Artificial Intelligence，2020，34（4）：3930-3937.
[20] WU J L，LIN Z C，ZHA H B.Essential tensor learning for multi-view spectral clustering[J].IEEE Transactions on Image Processing，2019，28（12）：5910-5922.
[21] 程士卿，郝问裕，李晨，等.低秩张量分解的多视角谱聚类算法[J].西安交通大学学报，2020，54（3）：119-125.
CHENG S Q，HAO W Y，LI C，et al.Multi-view clustering by low-rank tensor decomposition[J].Journal of Xi’an Jiaotong University，2020，54（3）：119-125.
[22] KILMER M E，BRAMAN K S，HAO N，et al.Third-order tensors as operators on matrices：A theoretical and computational framework with applications in imaging[J].SIAM Journal on Matrix Analysis and Applications，2013，34（1）：148-172.
[23] SHAHID N，KALOFOLIAS V，BRESSON X，et al.Robust principal component analysis on graphs[C]//Proceedings of IEEE International Conference on Computer Vision，2015：2812-2820.
[24] LIN Z C，LIU R S，SU Z X.Linearized alternating direction method with adaptive penalty for low-rank representation[C]//Proceedings of the Neural Information Processing Systems，2011：612-620.
[25] HONG Y，WANG X C，WANG G Y，et al.An active three-way clustering method via low-rank matrices for multi-view data[J].Information Sciences，2018，507：823-839.
[26] DU S Q，MA Y D，MA Y R.Graph regularized compact low rank representation for subspace clustering[J].Knowledge-Based Systems，2016，118：56-69.
[27] WANG S Q，CHEN Y Y，JIN Y，et al.Error-robust low-rank tensor approximation for multi-view clustering[J].Knowledge-Based Systems，2021，215（9）：106745.
[28] ZHOU D Y，HUANG J Y，SCHOLKOPF B.Learning from labeled and unlabeled data on a directed graph[C]//Proceedings of International Conference on Machine Learning，2005：1036-1043.
[29] CHEN Y Y，XIAO X L，HUA Z Y，et al.Adaptive transition probability matrix learning for multiview spectral clustering[J].IEEE Transactions on Neural Networks and Learning Systems，2021，99：1-15.
[30] HU W R，TAO D C，ZHANG W S，et al.The twist tensor nuclear norm for video completion[J].IEEE Transactions on Neural Networks and Learning Systems，2017，28（12）：2961-2973.