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Multi-view clustering with filtered bipartite graph

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Abstract

The key challenge of graph-based multi-view clustering methods lies in how to capture a consensus clustering structure. Although existing methods have achieved good performances, they still share the following limitations: 1) The high computational complexity caused by large graph leaning. 2) The contaminated information in different views reduces the consistency of the fused graph. 3) The two-stage clustering strategy leads to sub-optimal solutions and error accumulation. To solve the above issues, we propose a novel multi-view clustering algorithm termed Multi-View Clustering with Filtered Bipartite Graph (MVC-FBG). In the graph construction stage, we select representative anchors to construct anchor graphs with less space complexity. Then we explicitly filter out the contaminated information to preserve the consistency in different views. Moreover, a low-rank constraint is imposed on the Laplacian matrix of the unified graph to obtain the clustering results directly. Furthermore, we design an efficient alternating optimization algorithm to solve our model, which enjoys a linear time complexity that can scale well with the data size. Extensive experimental results on different scale datasets demonstrate the effectiveness and efficiency of our proposed method.

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Data Availability

The data that support the findings of this study are openly available.

Notes

  1. http://research.microsoft.com/en us/projects/objectclassrecognition

  2. http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php

  3. https://archive.ics.uci.edu/ml/datasets/One-hundred+plant+species+leaves+data+set.

  4. http://archive.ics.uci.edu/ml/datasets/Multiple+Features

  5. http://www.vision.caltech.edu/Image\(\_\)Datasets/Caltech101/

  6. http://elki.dbs.ifi.lmu.de/wiki/DataSets/MultiView

References

  1. Cao X, Zhang C, Zhou C, Fu H, Foroosh H (2015) Constrained multi-view video face clustering. IEEE Trans Image Process 24(11):4381–4393

    MathSciNet  MATH  Google Scholar 

  2. Dhillon IS (2001) Co-clustering documents and words using bipartite spectral graph partitioning. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, pp 269–274

  3. Xu C, Tao D, Xu C (2013) A survey on multi-view learning. arXiv:1304.5634

  4. Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vis 60(2):91–110

    MATH  Google Scholar 

  5. Dalal N, Triggs B (2005) Histograms of oriented gradients for human detection. In: Proceedings of the IEEE conference on computer vision and pattern recognition, vol 1, pp 886–893. Ieee

  6. Ojala T, Pietikainen M, Maenpaa T (2002) Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans Pattern Anal Mach Intell 24(7):971–987

    MATH  Google Scholar 

  7. Zhao J, Li Y (2023) Binary multi-view sparse subspace clustering. Neural Comput Appl 35(29):21751–21770

    MATH  Google Scholar 

  8. Zhao L, Ma Y, Chen S, Zhou J (2023) Multi-view co-clustering with multi-similarity. Appl Intell 53(13):16961–16972

    Google Scholar 

  9. Wang S, Wang Y, Lu G, Le W (2023) Mixed structure low-rank representation for multi-view subspace clustering. Appl Intell 53(15):18470–18487

    MATH  Google Scholar 

  10. Sun F, Xie X, Qian J, Xin Y, Li Y, Wang C, Chao G (2022) Multi-view k-proximal plane clustering. Appl Intell 52(13):14949–14963

    Google Scholar 

  11. Zhang X, Yang Y, Li T, Zhang Y, Wang H, Fujita H (2021) Cmc: a consensus multi-view clustering model for predicting alzheimer’s disease progression. Comput Methods Prog Biomed 199:105895

    MATH  Google Scholar 

  12. Wang H, Yang Y, Liu B, Fujita H (2019) A study of graph-based system for multi-view clustering. Knowl-Based Syst 163:1009–1019

    MATH  Google Scholar 

  13. Zhan K, Zhang C, Guan J, Wang J (2017) Graph learning for multiview clustering. IEEE Trans Cybern 48(10):2887–2895

    MATH  Google Scholar 

  14. Zhan K, Niu C, Chen C, Nie F, Zhang C, Yang Y (2018) Graph structure fusion for multiview clustering. IEEE Trans Knowl Data Eng 31(10):1984–1993

    MATH  Google Scholar 

  15. Nie F, Li J, Li X, et al (2017) Self-weighted multiview clustering with multiple graphs. In: Proceedings of the twenty-sixth international joint conference on artificial intelligence, pp 2564–2570

  16. Tong H, He J, Li M, Zhang C, Ma W-Y (2005) Graph based multi-modality learning. In: Proceedings of the 13th annual ACM international conference on multimedia, pp 862–871

  17. Li Y, Nie F, Huang H, Huang J (2015) Large-scale multi-view spectral clustering via bipartite graph. In: Proceedings of the AAAI conference on artificial intelligence, pp 2750–2756

  18. Xiao Q, Du S, Zhang K, Song J, Huang Y (2023) Adaptive sparse graph learning for multi-view spectral clustering. Appl Intell 53(12):14855–14875

    MATH  Google Scholar 

  19. Wong WK, Han N, Fang X, Zhan S, Wen J (2019) Clustering structure-induced robust multi-view graph recovery. IEEE Trans Circ Syst Video Technol 30(10):3584–3597

    MATH  Google Scholar 

  20. Huang D, Wang C-D, Wu J-S, Lai J-H, Kwoh C-K (2019) Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans Knowl Data Eng 32(6):1212–1226

    MATH  Google Scholar 

  21. Yang B, Zhang X, Lin Z, Nie F, Chen B, Wang F (2022) Efficient and robust multiview clustering with anchor graph regularization. IEEE Trans Circ Syst Video Technol 32(9):6200–6213

    MATH  Google Scholar 

  22. Jiang G, Peng J, Wang H, Mi Z, Fu X (2022) Tensorial multi-view clustering via low-rank constrained high-order graph learning. IEEE Trans Circ Syst Video Technol 32(8):5307–5318

    MATH  Google Scholar 

  23. Nie F, Cai G, Li X (2017) Multi-view clustering and semi-supervised classification with adaptive neighbours. In: Proceedings of the thirty-first AAAI conference on artificial intelligence, pp 2408–2414

  24. Hu Y, Song Z, Wang B, Gao J, Sun Y, Yin B (2021) Akm 3 c: Adaptive k-multiple-means for multi-view clustering. IEEE Trans Circ Syst Video Technol 31(11):4214–4226

    MATH  Google Scholar 

  25. Cao X, Zhang C, Fu H, Liu S, Zhang H (2015) Diversity-induced multi-view subspace clustering. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 586–594

  26. Gao H, Nie F, Li X, Huang H (2015) Multi-view subspace clustering. In: Proceedings of the IEEE international conference on computer vision, pp 4238–4246

  27. Li B, Lu H, Zhang Y, Lin Z, Wu W (2018) Subspace clustering under complex noise. IEEE Trans Circ Syst Video Technol 29(4):930–940

    MATH  Google Scholar 

  28. Luo S, Zhang C, Zhang W, Cao X (2018) Consistent and specific multi-view subspace clustering. In: Proceedings of the AAAI conference on artificial intelligence, vol 32, pp 3730–3737

  29. Li B, Lu H, Li F, Wu W (2016) Subspace clustering with \( k \)-support norm. IEEE Trans Circ Syst Video Technol 28(2):302–313

    MATH  Google Scholar 

  30. Wang M, Hua X-S, Yuan X, Song Y, Dai L-R (2007) Optimizing multi-graph learning: Towards a unified video annotation scheme. In: Proceedings of the 15th ACM international conference on multimedia, pp 862–871

  31. Xia T, Tao D, Mei T, Zhang Y (2010) Multiview spectral embedding. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 40(6):1438–1446

  32. Huang H-C, Chuang Y-Y, Chen C-S (2012) Affinity aggregation for spectral clustering. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 773–780. IEEE

  33. Karasuyama M, Mamitsuka H (2013) Multiple graph label propagation by sparse integration. IEEE Trans Neural Netw Learn Syst 24(12):1999–2012

    MATH  Google Scholar 

  34. Nie F, Li J, Li X, et al (2016) Parameter-free auto-weighted multiple graph learning: A framework for multiview clustering and semi-supervised classification. In: Proceedings of the twenty-fifth international joint conference on artificial intelligence, pp 1881–1887

  35. Nie F, Cai G, Li J, Li X (2017) Auto-weighted multi-view learning for image clustering and semi-supervised classification. IEEE Trans Image Process 27(3):1501–1511

    MathSciNet  MATH  Google Scholar 

  36. Wang R, Nie F, Wang Z, Hu H, Li X (2019) Parameter-free weighted multi-view projected clustering with structured graph learning. IEEE Trans Knowl Data Eng 32(10):2014–2025

    MATH  Google Scholar 

  37. Nie F, Wang X, Jordan M, Huang H (2016) The constrained laplacian rank algorithm for graph-based clustering. In: Proceedings of the AAAI conference on artificial intelligence vol 30, pp 1969–1976

  38. Jia Y, Liu H, Hou J, Kwong S, Zhang Q (2021) Multi-view spectral clustering tailored tensor low-rank representation. IEEE Trans Circ Syst Video Technol 31(12):4784–4797

    MATH  Google Scholar 

  39. Lan M, Meng M, Yu J, Wu J (2022) Generalized multi-view collaborative subspace clustering. IEEE Trans Circ Syst Video Technol 32(6):3561–3574

    MATH  Google Scholar 

  40. Liang Y, Huang D, Wang C-D (2019) Consistency meets inconsistency: A unified graph learning framework for multi-view clustering. In: 2019 IEEE international conference on data mining (ICDM), pp 1204–1209. IEEE

  41. Horie M, Kasai H (2021) Consistency-aware and inconsistency-aware graph-based multi-view clustering. In: 2020 European signal processing conference (EUSIPCO), pp 1472–1476. IEEE

  42. Tang Y, Xie Y, Zhang W (2023) Affine subspace robust low-rank self-representation: from matrix to tensor. IEEE Trans Pattern Anal Mach Intell 45(8):9357–9373

    MATH  Google Scholar 

  43. Guo J, Sun Y, Gao J, Hu Y, Yin B (2022) Logarithmic schatten-\( p \) p norm minimization for tensorial multi-view subspace clustering. IEEE Trans Pattern Anal Mach Intell 45(3):3396–3410

    MATH  Google Scholar 

  44. Zhang B, Qiang Q, Wang F, Nie F (2020) Fast multi-view semi-supervised learning with learned graph. IEEE Trans Knowl Data Eng 34(1):286–299

    MATH  Google Scholar 

  45. Li L, He H (2020) Bipartite graph based multi-view clustering. IEEE Trans Knowl Data Eng 34(7):3111–3125

    MATH  Google Scholar 

  46. Liu S, Liang K, Dong Z, Wang S, Yang X, Zhou S, Zhu E, Liu X (2024) Learn from view correlation: An anchor enhancement strategy for multi-view clustering. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp 26151–26161

  47. Zhang C, Jia X, Li Z, Chen C, Li H (2024) Learning cluster-wise anchors for multi-view clustering. In: Proceedings of the AAAI conference on artificial intelligence vol 38, pp 16696–16704

  48. Kang Z, Zhou W, Zhao Z, Shao J, Han M, Xu Z (2020) Large-scale multi-view subspace clustering in linear time. In: Proceedings of the AAAI conference on artificial intelligence vol 34, pp 4412–4419

  49. Zhu W, Nie F, Li X (2017) Fast spectral clustering with efficient large graph construction. In: 2017 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 2492–2496. IEEE

  50. Li X, Zhang H, Wang R, Nie F (2020) Multiview clustering: A scalable and parameter-free bipartite graph fusion method. IEEE Trans Pattern Anal Mach Intell 44(1):330–344

    MATH  Google Scholar 

  51. Sun M, Zhang P, Wang S, Zhou S, Tu W, Liu X, Zhu E, Wang C (2021) Scalable multi-view subspace clustering with unified anchors. In: Proceedings of the 29th ACM international conference on multimedia, pp 3528–3536

  52. Ji J, Feng S (2023) Anchor structure regularization induced multi-view subspace clustering via enhanced tensor rank minimization. In: Proceedings of the IEEE/CVF international conference on computer vision, pp 19343–19352

  53. Wang S, Liu X, Liu S, Jin J, Tu W, Zhu X, Zhu E (2022) Align then fusion: Generalized large-scale multi-view clustering with anchor matching correspondences. Adv Neural Inf Process Syst 35:5882–5895

    MATH  Google Scholar 

  54. Bojchevski A, Matkovic Y, Günnemann S (2017) Robust spectral clustering for noisy data: Modeling sparse corruptions improves latent embeddings. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, pp 737–746

  55. Newman MW, Libraty N, On O, On KA, On KA (1991) The laplacian spectrum of graphs. Graph Theory, Combinations and Applications 18(7):871–898

    MathSciNet  MATH  Google Scholar 

  56. Fan K (1949) On a theorem of weyl concerning eigenvalues of linear transformations i. Proc National Academy Sci 35(11):652–655

    MathSciNet  MATH  Google Scholar 

  57. Wang H, Yang Y, Liu B (2019) Gmc: Graph-based multi-view clustering. IEEE Trans Knowl Data Eng 32(6):1116–1129

    MATH  Google Scholar 

  58. Chua T.-S, Tang J, Hong R, Li H, Luo Z, Zheng Y (2009) Nus-wide: a real-world web image database from national university of singapore. In: Proceedings of the ACM international conference on image and video retrieval, pp 1–9

  59. Von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416

    MathSciNet  MATH  Google Scholar 

  60. Nie F, Tian L, Li X (2018) Multiview clustering via adaptively weighted procrustes. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, pp 2022–2030

  61. Kumar A, Rai P, Daume H (2011) Co-regularized multi-view spectral clustering. Adv Neural Inf Process Syst 24:1413–1421

    MATH  Google Scholar 

  62. Zhan K, Nie F, Wang J, Yang Y (2018) Multiview consensus graph clustering. IEEE Trans Image Process 28(3):1261–1270

    MathSciNet  MATH  Google Scholar 

  63. Xia R, Pan Y, Du L, Yin J (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Proceedings of the AAAI conference on artificial intelligence vol 28, pp 2149–2155

  64. Zong L, Zhang X, Liu X, Yu H (2018) Weighted multi-view spectral clustering based on spectral perturbation. In: Proceedings of the AAAI conference on artificial intelligence vol 32, pp 4621–4629

  65. Wan X, Liu X, Liu J, Wang S, Wen Y, Liang W, Zhu E, Liu Z, Zhou L (2023) Auto-weighted multi-view clustering for large-scale data. In: Proceedings of the AAAI Conference on Artificial Intelligence vol 37, pp 10078–10086

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Authors and Affiliations

  1. School of Computer Science and Technology, Beijing Jiaotong University, Beijing, 100044, China

    Jintian Ji & Songhe Feng

  2. Normal College, Beijing Union University, Beijing, 100101, China

    Hailei Peng

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  1. Jintian Ji
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  2. Hailei Peng
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  3. Songhe Feng
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Contributions

Jintian Ji and Songhe Feng contributed to the conception of the study, performed the experiment, the data analyses, and wrote the manuscript. Hailei Peng contributed significantly to analysis and manuscript preparation. All authors reviewed the manuscript.

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Correspondence to Hailei Peng.

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Ji, J., Peng, H. & Feng, S. Multi-view clustering with filtered bipartite graph. Appl Intell 55, 570 (2025). https://doi.org/10.1007/s10489-025-06476-4

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