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Structured anchor-inferred graph learning for universal incomplete multi-view clustering

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Abstract

The goal of multi-view spectral clustering (MVSC) is to explore the intrinsic cluster structures embedded in the multi-view data and group the learned optimal feature embeddings into different clusters based on similarity measurement. Although encouraging improvements have been achieved, when facing the incomplete multi-view data, these MVSC methods would be disabled since most of them are generally built on the common assumption that data is required to have complete multiple descriptions, which obviously violates real-world situations. In this paper, we propose a novel Structured Anchor-inferred Graph Learning (SAGL) method to tackle the challenging universal incomplete multi-view spectral clustering problem, which can handle arbitrary view missing cases. Specifically, instead of using the fixed distance-based weighting matrix in the existing incomplete MVSC, we construct a structural anchor-based similarity learning model to formulate a learnable asymmetric intra-view similarity matrix. Meanwhile, the inter-view similarities can be successfully bridged by the paired anchor samples, which can skillfully overcome the limitation of insufficient information operations on incomplete multi-view data. Particularly, we further extend the two-view cases to the late fusion version of universal cases for accurate similarity calculation on incomplete multi-view data. Moreover, we derive a complete anchor-inferred graph learning scheme to enhance the efficiency of the spectral clustering process, which can well capture the hidden connection information among multi-view data, yielding improved clustering performance. Furthermore, we design a fast learning algorithm to solve the resulting optimization problem. Extensive experiments on multiple multi-view datasets show the superiority and advantages of the proposed method when handling different types of multi-view data with arbitrary information missing.

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Notes

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

  2. http://www.robots.ox.ac.uk/vgg/data/flowers/

  3. http://www.vision.caltech.edu/ImageDatasets/Caltech101/

  4. http://mlg.ucd.ie/datasets/3Sources.html

References

  1. Zhang, Z., Xu, Y., Shao, L., Yang, J.: Discriminative block-diagonal representation learning for image recognition. IEEE Transactions on Neural Networks and Learning Systems 29(7), 3111–3125 (2017)

    Article  Google Scholar 

  2. Li, Z., Zhang, Z., Qin, J., Zhang, Z., Shao, L.: Discriminative fisher embedding dictionary learning algorithm for object recognition. IEEE Transactions on Neural Networks and Learning Systems 31(3), 786–800 (2019)

    Article  Google Scholar 

  3. Zhang, Z., Liu, L., Shen, F., Shen, H.T., Shao, L.: Binary multi-view clustering. IEEE Trans. Pattern Anal. Mach. Intell. 41(7), 1774–1782 (2018)

    Article  Google Scholar 

  4. Du, J., Michalska, S., Subramani, S., Wang, H., Zhang, Y.: Neural attention with character embeddings for hay fever detection from twitter. Health Information Science and Systems 7(1), 1–7 (2019)

    Article  Google Scholar 

  5. Zhang, Z., Liu, L., Luo, Y., Huang, Z., Shen, F., Shen, H.T., Lu, G.: Inductive structure consistent hashing via flexible semantic calibration. IEEE Transactions on Neural Networks and Learning Systems 32(10), 4514–4528 (2020)

    Article  Google Scholar 

  6. Chen, J., Zhong, M., Li, J., Wang, D., Qian, T., Tu, H.: Effective deep attributed network representation learning with topology adapted smoothing. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2021.3064092 (2021)

  7. Xue, G., Zhong, M., Li, J., Chen, J., Zhai, C., Kong, R. (2021)

  8. Li, Z., Wang, X., Li, J., Zhang, Q.: Deep attributed network representation learning of complex coupling and interaction. Knowl.-Based Syst. 212, 106618 (2021)

    Article  Google Scholar 

  9. Yang, Y., Guan, Z., Li, J., Zhao, W., Cui, J., Wang, Q.: Interpretable and efficient heterogeneous graph concolutional network. IEEE Transactions on Knowledge and Data Engineering. https://doi.org/10.1109/TKDE.2021.3101356 (2021)

  10. Yin, H., Yang, S., Song, X., Liu, W., Li, J.: Deep fusion of multimodal features for social media retweet time prediction. World Wide Web 24(4), 1027–1044 (2021)

    Article  Google Scholar 

  11. Haldar, N.A.H., Reynolds, M., Shao, Q., Paris, C., Li, J., Chen, Y.: Activity location inference of users based on social relationship. World Wide Web, pp. 1–19 (2021)

  12. Cai, T., Li, J., Mian, A.S., Sellis, T., Yu, J.X., et al.: Target-aware holistic influence maximization in spatial social networks. IEEE Transactions on Knowledge and Data Engineering. https://doi.org/10.1109/TKDE.2020.3003047 (2020)

  13. Hou, C., Zhou, Z.H.: One-pass learning with incremental and decremental features. IEEE Trans. Pattern Anal. Mach. Intell. 40(11), 2776–2792 (2018)

    Article  Google Scholar 

  14. Hou, C., Zeng, L.L., Hu, D.: Safe classification with augmented features. IEEE Transactions on Pattern Analysis and Machine Intelligence PP, 1–1 (2018)

    Google Scholar 

  15. Zhang, Z., Liu, L., Qin, J., Zhu, F., Shen, F., Xu, Y., Shao, L., Shen, H.T.: Highly-economized multi-view binary compression for scalable image clustering. In: Proceedings of the European Conference on Computer Vision (ECCV), pp 717–732 (2018)

  16. Hartigan, J.A., Wong, M.A.: Algorithm as 136: A k-means clustering algorithm. Journal of the Royal Statistical Society. Ser. C (Appl. Stat.) 28(1), 100–108 (1979)

    MATH  Google Scholar 

  17. Chen, Y., Xiao, X., Peng, C., Lu, G., Zhou, Y.: Low-rank tensor graph learning for multi-view subspace clustering. IEEE Transactions on Circuits and Systems for Video Technology 32(1), 92–104 (2021)

    Article  Google Scholar 

  18. Li, J., Cai, T., Deng, K., Wang, X., Sellis, T., Xia, F.: Community-diversified influence maximization in social networks. Inf. Syst. 92, 101522 (2020)

    Article  Google Scholar 

  19. Chen, Y., Wang, S., Peng, C., Hua, Z., Zhou, Y.: Generalized nonconvex low-rank tensor approximation for multi-view subspace clustering. IEEE Trans. Image Process. 30, 4022–4035 (2021)

    Article  Google Scholar 

  20. Chen, Y., Xiao, X., Hua, Z., Zhou, Y.: Adaptive transition probability matrix learning for multiview spectral clustering. IEEE Transactions on Neural Networks and Learning Systems. https://doi.org/10.1109/TNNLS.2021.3059874 (2021)

  21. Cai, X., Nie, F., Huang, H.: Multi-view K-means clustering on big data. In: Twenty-third International joint conference on artificial intelligence (2013)

  22. Xu, J., Han, J., Nie, F.: Discriminatively embedded k-means for multi-view clustering. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 5356–5364 (2016)

  23. Zhao, B., Kwok, J.T., Zhang, C.: Multiple kernel clustering. In: Proceedings of the 2009 SIAM International Conference on Data Mining, pp 638–649. SIAM (2009)

  24. Lu, Y., Wang, L., Lu, J., Yang, J., Shen, C.: Multiple kernel clustering based on centered kernel alignment. Pattern Recogn. 47(11), 3656–3664 (2014)

    Article  MATH  Google Scholar 

  25. Kumar, A., Daumé, H.: A co-training approach for multi-view spectral clustering. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp 393–400. Citeseer (2011)

  26. Gao, H., Nie, F., Li, X., Huang, H.: Multi-view subspace clustering. In: Proceedings of the IEEE International Conference on Computer Vision, pp 4238–4246 (2015)

  27. Zhang, C., Fu, H., Hu, Q., Cao, X., Xie, Y., Tao, D., Xu, D.: Generalized latent multi-view subspace clustering. IEEE transactions on pattern analysis and machine intelligence 42(1), 86–99 (2018)

    Article  Google Scholar 

  28. Li, Z., Wang, Q., Tao, Z., Gao, Q., Yang, Z.: Deep adversarial multi-view clustering network. In: IJCAI, pp 2952–2958 (2019)

  29. Huang, Z., Zhou, J.T., Peng, X., Zhang, C., Zhu, H., Lv, J.: Multi-view spectral clustering network. In: IJCAI, pp 2563–2569 (2019)

  30. Cheng, M., Jing, L.: Ng, M.K., Tensor-based low-dimensional representation learning for multi-view clustering (2019)

  31. Tang, Y., Xie, Y., Zhang, C., Zhang, Z., Zhang, W.: One-step multiview subspace segmentation via joint skinny tensor learning and latent clustering. IEEE Transactions on Cybernetics PP(99), 1–15 (2021)

    Google Scholar 

  32. Tang, Y., Xie, Y., Yang, X., Niu, J., Zhang, W.: Tensor multi-elastic kernel self-paced learning for time series clustering. IEEE Trans Knowl Data Eng PP(99), 1–1 (2019)

    Google Scholar 

  33. Zhu, P., Hui, B., Zhang, C., Du, D., Wen, L., Hu, Q. (2019)

  34. Shao, W., He, L., Philip, S.Y.: Multiple incomplete views clustering via weighted nonnegative matrix factorization with l2,1 regularization. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp 318–334. Springer (2015)

  35. Shao, W., He, L., Lu, C.-t., Philip, S.Y.: Online multi-view clustering with incomplete views. In: 2016 IEEE International conference on big data (Big Data), pp 1012–1017. IEEE (2016)

  36. Li, S.-Y., Jiang, Y., Zhou, Z.-H.: Partial multi-view clustering. In: Proceedings of the AAAI conference on artificial intelligence, vol. 28 (2014)

  37. Rai, N., Negi, S., Chaudhury, S., Deshmukh, O.: Partial multi-view clustering using graph regularized Nmf. In: 2016 23rd International conference on pattern recognition (ICPR). https://doi.org/10.1109/ICPR.2016.7899961, pp 2192–2197 (2016)

  38. Zhao, H., Liu, H., Fu, Y.: Incomplete Multi-Modal Visual Data Grouping. In: IJCAI, pp 2392–2398 (2016)

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

  40. Zhang, C., Fu, H., Liu, S., Liu, G., Cao, X.: Low-rank tensor constrained multiview subspace clustering. In: Proceedings of the IEEE International Conference on Computer Vision, pp 1582–1590 (2015)

  41. Wang, X., Guo, X., Lei, Z., Zhang, C., Li, S.Z.: Exclusivity-consistency regularized multi-view subspace clustering. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 92–931 (2017)

  42. An, J., Luo, H., Zhang, Z., Zhu, L., Lu, G.: Cognitive multi-modal consistent hashing with flexible semantic transformation. Information Processing & Management 59(1), 102743 (2022)

    Article  Google Scholar 

  43. Nie, F., Huang, H., Cai, X., Ding, C.: Efficient and robust feature selection via joint l2,1-norms minimization. Advances in nerual information processing systems 23, 1813–1821 (2010)

  44. Nie, F., Wang, X., Deng, C., Huang, H.: Learning a structured optimal bipartite graph for co-clustering. In: Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 4132–4141 (2017)

  45. Guo, J., Ye, J.: Anchors bring ease: an embarrassingly simple approach to partial multi-view clustering. In: Proceedings of the AAAI conference on artificial intelligence, vol. 33, pp 118–125 (2019)

  46. Wang, R., Nie, F., Yu, W.: Fast spectral clustering with anchor graph for large hyperspectral images. IEEE Geosci. Remote Sens. Lett. 14(11), 2003–2007 (2017)

    Article  Google Scholar 

  47. Liu, W., Wang, J., Kumar, S., Chang, S.-F.: Hashing with Graphs. In: International conference on machine learning, pp 1–7 (2011)

  48. Dua, D., Graff, C.: UCI Machine Learning Repository. https://doi.org/http://archive.ics.uci.edu/ml (2017)

  49. Wen, J., Zhang, Z., Zhang, Z., Fei, L., Wang, M.: Generalized incomplete multiview clustering with flexible locality structure diffusion. IEEE transactions on cybernetics 51(1), 101–114 (2020)

    Article  Google Scholar 

  50. Kang, Z., Lin, Z., Zhu, X., Xu, W.: Structured graph learning for scalable subspace clustering: From single view to multiview. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2021.3061660 (2021)

  51. Hu, M., Chen, S.: Doubly aligned incomplete multi-view clustering. arXiv:1903.02785 (2019)

  52. Yang, C., Ren, Z., Sun, Q., Wu, M., Sun, Y.: Joint correntropy metric weighting and block diagonal regularizer for robust multiple kernel subspace clustering. Inform. Sci., 500 (2019)

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Acknowledgements

This work was supported in part by the NSFC fund no. 62002085 and 62106063, in part by the Shenzhen Fundamental Research Fund under no. GXWD20201230155427003-20200824103320001 and GXWD20201230155427003-20200824113231001.

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  1. School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, Shenzhen, 518055, China

    Wenjue He, Zheng Zhang, Yongyong Chen & Jie Wen

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  1. Wenjue He
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This article belongs to the Topical Collection: Special Issue on Decision Making in Heterogeneous Network Data Scenarios and Applications

Guest Editors: Jianxin Li, Chengfei Liu, Ziyu Guan, and Yinghui Wu

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He, W., Zhang, Z., Chen, Y. et al. Structured anchor-inferred graph learning for universal incomplete multi-view clustering. World Wide Web 26, 375–399 (2023). https://doi.org/10.1007/s11280-022-01012-7

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