Abstract
Multi-view clustering (MVC) algorithms usually have good performance which benefits from the merit that multi-view data contains more comprehensive information. Generally, most graph-based MVC algorithms adopt a two-step learning strategy, that is, first learn affinity graphs from each view, and then fuse these graphs according to certain criterion to obtain the final consistent affinity graph. Although this strategy can get partial consistent information from multiple views, it still suffers from some drawbacks. 1) Due to the existence of noise and redundant features in the raw data, the structural information in the learned affinity graphs may deviate from the truth; 2) The affinity graphs learned in the first step may constrain each other in the fusion stage, which may lead to further degradation of the final affinity graph. To minimize the impact of the above factors, a new MVC method, multi-view latent structure learning with rank recovery (MLSL), is proposed in this work. Specifically, MLSL recovers a set of low-rank representations from the raw data by low-rank matrix approximation, then learns a consistent embedding space of the raw data from these new representations, and finally learns adaptively the inherent affinity graph from the learned embedding space. In the learning process of MLSL, the low-rank recovery is used to remove the noise of the raw data, the embedding space learning is used to minimize the redundant features, and the single affinity graph learning can avoid graph fusion. Meanwhile, orthogonal constraints are used to ensure that the embedding space have the same rank as the low-rank representations of each view. Schatten p-norm is adopted in low-rank recovery technology to better approximate the rank of matrix. An efficient iterative algorithm is designed to solve the non-convex optimization problem based on the Schatten p −norm. Finally, extensive experiments on nine datasets are performed to evaluate the performance of the proposed algorithm. The experimental results indicate that MLSL can improve the clustering performance on most datasets compared with related recent studies. Meanwhile, the ablation experiments also verify that the low-rank recovery policy in MLSL can improve the multi-view clustering performance.
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Zhang Z, Wang M (2022) Multi-feature fusion partitioned local binary pattern method for finger vein recognition. Signal Image Video Process, 1–9
Giveki D, Soltanshahi MA, Montazer GA (2017) A new image feature descriptor for content based image retrieval using scale invariant feature transform and local derivative pattern. Optik 131:242–254
Erazo-Aux J, Loaiza-Correa H, Restrepo-Giron A (2019) Histograms of oriented gradients for automatic detection of defective regions in thermograms. Appl Opt 58(13):3620–3629
Zhao J, Xie X, Xu X, Sun S (2017) Multi-view learning overview: recent progress and new challenges. Inform Fus 38:43–54
Yang Y, Wang H (2018) Multi-view clustering: a survey. Big Data Mining and Analytics 1 (2):83–107
Yang M, Deng C, Nie F (2019) Adaptive-weighting discriminative regression for multi-view classification. Pattern Recogn 88:236–245
Shu T, Zhang B, Tang YY (2019) Multi-view classification via a fast and effective multi-view nearest-subspace classifier. IEEE Access 7:49669–49679
Cheng X, Zhu Y, Song J, Wen G, He W (2017) A novel low-rank hypergraph feature selection for multi-view classification. Neurocomputing 253:115–121
Yang MS, Sinaga KP (2019) A feature-reduction multi-view k-means clustering algorithm. IEEE Access 7:114472–114486
Zhang H, Wu D, Nie F, Wang R, Li X (2021) Multilevel projections with adaptive neighbor graph for unsupervised multi-view feature selection. Inform Fus 70:129–140
Yin Q, Zhang J, Wu S, Li H (2019) Multi-view clustering via joint feature selection and partially constrained cluster label learning. Pattern Recogn 93:380–391
Li Z, Hu Z, Nie F, Wang R, Li X (2022) Multi-view clustering based on generalized low rank approximation. Neurocomputing 471:251–259
Fu X, Huang K, Papalexakis EE, Song H, Talukdar P, Sidiropoulos ND, Faloutsos C, Mitchell T (2018) Efficient and distributed generalized canonical correlation analysis for big multiview data. IEEE Trans Knowl Data Eng 31(12):2304–2318
Tan H, Zhang X, Lan L, Huang X, Luo Z (2019) Nonnegative constrained graph based canonical correlation analysis for multi-view feature learning. Neural Process Lett 50(2):1215–1240
Cai W, Zhou H, Xu L (2021) A multi-view co-training clustering algorithm based on global and local structure preserving. IEEE Access 9:29293–29302
Chen M, Li X (2021) Robust matrix factorization with spectral embedding. IEEE Trans Neur Netw Learn Syst 32:5698–5707
Liu B, Chen X, Xiao Y, Li W, Liu L, Liu C (2021) An efficient dictionary-based multi-view learning method. Inform Sci 576:157–172
Aghdam MH, Zanjani MD (2021) A novel regularized asymmetric non-negative matrix factorization for text clustering. Inform Process Manag 58(6):102694
Liang N, Yang Z, Li Z, Sun W, Xie S (2020) Multi-view clustering by non-negative matrix factorization with co-orthogonal constraints. Knowl-Based Syst 194:105582
Liu X, Pan G, Xie M (2021) Multi-view subspace clustering with adaptive locally consistent graph regularization. Neural Comput Applic, 1–16
Jing P, Su Y, Li Z, Nie L (2021) Learning robust affinity graph representation for multi-view clustering. Inform Sci 544:155–167
Zhou P, Du L, Li X, Shen Y-D, Qian Y (2020) Unsupervised feature selection with adaptive multiple graph learning. Pattern Recogn 105:107375
Yu X, Liu H, Wu Y, Zhang C (2021) Fine-grained similarity fusion for multi-view spectral clustering. Inform Sci 568:350–368
Dai J, Ren Z, Luo Y, Song H, Yang J (2021) Multi-view clustering with latent low-rank proxy graph learning. Cogn Comput, 1–12
Chen M-S, Huang L, Wang C-D, Huang D, Lai J-H (2021) Relaxed multi-view clustering in latent embedding space. Inform Fus 68:8–21
Mi Y, Ren Z, Mukherjee M, Huang Y, Sun Q, Chen L (2021) Diversity and consistency embedding learning for multi-view subspace clustering. Appl Intell, 1–14
Luo P, Peng J, Guan Z, Fan J (2018) Dual regularized multi-view non-negative matrix factorization for clustering. Neurocomputing 294:1–11
Ma J, Yuan Y (2019) Dimension reduction of image deep feature using pca. J Vis Commun Image Represent 63:102578
Rong W, Zhuo E, Peng H, Chen J, Wang H, Han C, Cai H (2021) Learning a consensus affinity matrix for multi-view clustering via subspaces merging on grassmann manifold. Inform Sci 547:68–87
Mei Y, Ren Z, Wu B, Shao Y, Yang T (2021) Robust graph-based multi-view clustering in latent embedding space. Int J Mach Learn Cybern, 1–12
Fan R, Luo T, Zhuge W, Qiang S, Hou C (2020) Multi-view subspace learning via bidirectional sparsity. Pattern Recogn 108:107524
Li Z, Hu Z, Nie F, Wang R, Li X (2022) Multi-view clustering based on generalized low rank approximation. Neurocomputing 471:251–259
Fornasier M, Maly J, Naumova V (2021) Robust recovery of low-rank matrices with non-orthogonal sparse decomposition from incomplete measurements. Appl Math Comput 392:125702
Zheng Q, Zhu J, Tian Z, Li Z, Pang S, Jia X (2020) Constrained bilinear factorization multi-view subspace clustering. Knowl-Based Syst 194:105514
Yu S, Yiquan W (2018) Subspace clustering based on latent low rank representation with frobenius norm minimization. Neurocomputing 275:2479–2489
Zhuge W, Nie F, Hou C, Yi D (2017) Unsupervised single and multiple views feature extraction with structured graph. IEEE Trans Knowl Data Eng 29(10):2347–2359
Brbić M, Kopriva I (2018) Multi-view low-rank sparse subspace clustering. Pattern Recogn 73:247–258
Wang H, Yang Y, Liu B (2019) Gmc: graph-based multi-view clustering. IEEE Trans Knowl Data Eng 32(6):1116–1129
Zheng Q, Zhu J, Li Z, Pang S, Wang J, Li Y (2020) Feature concatenation multi-view subspace clustering. Neurocomputing 379:89–102
Ma S, Zheng Q, Liu Y (2021) Essential multi-view graph learning for clustering. J Ambient Intell Humaniz Comput, 1–12
Hao W, Pang S, Chen Z (2021) Multi-view spectral clustering via common structure maximization of local and global representations. Neural Netw 143:595–606
Shi S, Nie F, Wang R, Li X (2022) Self-weighting multi-view spectral clustering based on nuclear norm. Pattern Recogn 124:108429
Li H, Ren Z, Mukherjee M, Huang Y, Sun Q, Li X, Chen L (2020) Robust energy preserving embedding for multi-view subspace clustering. Knowl-Based Syst 210:106489
Kang Z, Pan H, Hoi SC, Xu Z (2019) Robust graph learning from noisy data. IEEE Trans Cybern 50(5):1833–1843
Xie D, Gao Q, Wang Q, Zhang X, Gao X (2020) Adaptive latent similarity learning for multi-view clustering. Neural Netw 121:409–418
Zhang X, Ren Z, Sun H, Bai K, Feng X, Liu Z (2021) Multiple kernel low-rank representation-based robust multi-view subspace clustering. Inform Sci 551:324–340
Tang C, Chen J, Liu X, Li M, Wang P, Wang M, Lu P (2018) Consensus learning guided multi-view unsupervised feature selection. Knowl-Based Syst 160:49–60
Yun Y, Xia W, Zhang Y, Gao Q, Gao X (2021) Self-representation and class-specificity distribution based multi-view clustering. Neurocomputing 437:9–20
Pang Y, Xie J, Nie F, Li X (2018) Spectral clustering by joint spectral embedding and spectral rotation. IEEE Trans Cybern 50(1):247–258
Pal R, Chaitanya AK, Srinivas K (2019) Low-complexity beam selection algorithms for millimeter wave beamspace mimo systems. IEEE Commun Lett 23(4):768–771
Zhang G-Y, Zhou Y-R, He X-Y, Wang C-D, Huang D (2020) One-step kernel multi-view subspace clustering. Knowl-Based Syst 189:105126
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Nos. 61976182, 62076171, 61876157, 61976245), and Sichuan Key R&D project (2020YFG0035), the Natural Science Foundation of Sichuan Province (2022NSFSC0898).
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He, J., Chen, H., Li, T. et al. Multi-view latent structure learning with rank recovery. Appl Intell 53, 12647–12665 (2023). https://doi.org/10.1007/s10489-022-04141-8
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DOI: https://doi.org/10.1007/s10489-022-04141-8