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Semi-Supervised Classification of Graph Convolutional Networks with Laplacian Rank Constraints

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Abstract

Graph convolutional networks (GCNs), as an extension of classic convolutional neural networks (CNNs) in graph processing, have achieved good results in completing semi-supervised learning tasks. Traditional GCNs usually use fixed graph to complete various semi-supervised classification tasks, such as chemical molecules and social networks. Graph is an important basis for the classification of GCNs model, and its quality has a large impact on the performance of the model. For low-quality input graph, the classification results of the GCNs model are often not ideal. In order to improve the classification effect of GCNs model, we propose a graph learning method to generate high-quality topological graph, which is more suitable for GCNs model classification. We use the correlation between the data to generate a data similarity matrix, and apply Laplacian rank constraint to similarity matrix, so that the number of connected components of the topological graph is consistent with the number of categories of the original data. Experimental results on 10 real datasets show that our method is better than the comparison method in classification effect.

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Notes

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References

  1. Atwood J, Towsley D (2016) Diffusion-convolutional neural networks. In: Advances in neural information processing systems, pp. 1993–2001

  2. Battaglia PW, Hamrick JB, Bapst V, Sanchez-Gonzalez A, Zambaldi V, Malinowski M, Tacchetti A, Raposo D, Santoro A, Faulkner R, et al. (2018) Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261

  3. Belkin M, Niyogi P (2002). Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in neural information processing systems, pp. 585–591

  4. Boyd S, Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge

    Book  Google Scholar 

  5. Bruna J, Zaremba W, Szlam A, LeCun Y (2013) Spectral networks and locally connected networks on graphs. arXiv preprint arXiv:1312.6203

  6. Chung FRK, Graham FC (1997) Spectral graph theory, No. 92. American Mathematical Society, Providence

    Google Scholar 

  7. Defferrard M, Bresson X, Vandergheynst P (2016) Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in neural information processing systems, pp. 3844–3852

  8. Fan K (1949) On a theorem of weyl concerning eigenvalues of linear transformations i. Proc Natl Acad Sci United States Am 35(11):652

    Article  MathSciNet  Google Scholar 

  9. Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT press, Cambridge

    MATH  Google Scholar 

  10. Grone R, Merris R, Sunder VS (1990) The laplacian spectrum of a graph. SIAM J Matrix Anal Appl 11(2):218–238

    Article  MathSciNet  Google Scholar 

  11. Guo Y, Gao Y, Shen D (2016) Deformable MR prostate segmentation via deep feature learning and sparse patch matching. IEEE Trans Med Imaging 35(4):1077–1089

    Article  Google Scholar 

  12. Guo Y, Wu Z, Shen D (2019) Learning longitudinal classification-regression model for infant hippocampus segmentation. Neurocomputing. https://doi.org/10.1016/j.neucom.2019.01.108

    Article  Google Scholar 

  13. Hammond DK, Vandergheynst P, Gribonval R (2011) Wavelets on graphs via spectral graph theory. Appl Comput Harmon Anal 30(2):129–150

    Article  MathSciNet  Google Scholar 

  14. Hao S, Zhou Y, Guo Y (2020) A brief survey on semantic segmentation with deep learning. Neurocomputing. https://doi.org/10.1016/j.neucom.2019.11.118

    Article  Google Scholar 

  15. He K, Gkioxari G, Dollár Piotr, GR (2017) Mask r-cnn. In: Proceedings of the IEEE international conference on computer vision, pp. 2961–2969

  16. Henaff M, Bruna J, LeCun Y (2015) Deep convolutional networks on graph-structured data. arXiv preprint arXiv:1506.05163

  17. Hu R, Zhu X, Zhu Y, Gan J (2019) Robust svm with adaptive graph learning. World Wide Web 23(3):1945–1968

    Article  Google Scholar 

  18. Kang Z, Lu X, Lu Y, Peng C, Chen W, Xu Z (2020) Structure learning with similarity preserving. Neural Netw. https://doi.org/10.1016/j.neunet.2020.05.030

    Article  Google Scholar 

  19. Kang Z, Pan H, Hoi SCH, Xu Z (2020) Robust graph learning from noisy data. IEEE Trans Cybern 50(5):1833–1843

    Article  Google Scholar 

  20. Kang Z, Zhao X, Peng C, Zhu H, Zhou JT, Peng X, Chen W, Xu Z (2020) Partition level multiview subspace clustering. Neural Netw 122:279–288

    Article  Google Scholar 

  21. Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980

  22. Kipf TN, Welling M (2016) Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907

  23. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  24. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  25. van der Maaten L, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605

    MATH  Google Scholar 

  26. Merris R (1994) Laplacian matrices of graphs: a survey. Linear Algebra Appl 197:143–176

    Article  MathSciNet  Google Scholar 

  27. Micheli A (2009) Neural network for graphs: A contextual constructive approach. IEEE Trans Neural Netw 20(3):498–511

    Article  MathSciNet  Google Scholar 

  28. Monti F, Bronstein M, Bresson X (2017) Geometric matrix completion with recurrent multi-graph neural networks. In: Advances in Neural Information Processing Systems, pp. 3697–3707

  29. Nie F, Wang X, Huang H (2014) Clustering and projected clustering with adaptive neighbors. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 977–986,

  30. Nie F, Wang X, Jordan MI , Huang H (2016) The constrained laplacian rank algorithm for graph-based clustering. In: Thirtieth AAAI Conference on Artificial Intelligence

  31. Ren S, He K, Girshick R, Sun J (2015) Faster r-cnn: Towards real-time object detection with region proposal networks. In: Advances in neural information processing systems, pp 91–99

  32. Scarselli F, Gori M, Tsoi AC, Hagenbuchner M, Monfardini G (2008) The graph neural network model. IEEE Trans Neural Netw 20(1):61–80

    Article  Google Scholar 

  33. Shen HT, Liu L, Yang Y, Xu X, Huang Z, Shen F, Hong R (2020) Exploiting subspace relation in semantic labels for cross-modal hashing. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/TKDE.2020.2970050

    Article  Google Scholar 

  34. Shen HT, Zhu Y, Zheng W, Zhu X (2020) Half-quadratic minimization for unsupervised feature selection on incomplete data. IEEE Trans on Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3009632

    Article  Google Scholar 

  35. Wang Y (2020) Survey on deep multi-modal data analytics: Collaboration, rivalry and fusion. arXiv preprint arXiv:2006.08159

  36. Wang Y, Lin W, Lin X, Gao J (2018) Multiview spectral clustering via structured low-rank matrix factorization. IEEE Trans Neural Netwo Learn Syst 29(10):4833–4843

    Article  Google Scholar 

  37. Zhang C, Zhang Y, Zhang Wenjie, Lin X (2016) Inverted linear quadtree: Efficient top k spatial keyword search. IEEE Trans Knowl Data Eng 28(7):1706–1721

    Article  Google Scholar 

  38. Zhang C, Zhu L, Zhang S, Weiren Y (2020) Pac-gan: an effective pose augmentation scheme for unsupervised cross-view person re-identification. Neurocomputing 387:22–39

    Article  Google Scholar 

  39. Zhang S, Li X, Zong M, Zhu X, Cheng D (2017) Learning k for knn classification. ACM Trans Intell Syst Technol (TIST) 8(3):1–19

    Google Scholar 

  40. Zhou J, Cui G , Zhang Z, Yang C, Liu Z , Wang L, Li C, Sun M (2018) Graph neural networks: A review of methods and applications. arXiv preprint arXiv:1812.08434,

  41. Zhou Y, Tian L, Zhu C, Jin X, Sun Y (2020) Video coding optimization for virtual reality 360-degree source. J Sel Topics Signal Process 14(1):118–129

    Article  Google Scholar 

  42. Zhu X, Gan J, Guangquan L, Li J, Zhang S (2020) Spectral clustering via half-quadratic optimization. World Wide Web 23:1969–1988

    Article  Google Scholar 

  43. Zhu X, Yang J, Zhang C, Zhang S (2019) Efficient utilization of missing data in cost-sensitive learning. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/TKDE.2019.2956530

    Article  Google Scholar 

  44. Zhu X, Zhang S, Zhu Y, Zhu P, Gao Y (2020) Unsupervised spectral feature selection with dynamic hyper-graph learning. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/TKDE.2020.3017250

    Article  Google Scholar 

  45. Zhu X, Zhu Y, Zheng W (2019) Spectral rotation for deep one-step clustering. Pattern Recognit 105:107175

    Article  Google Scholar 

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Acknowledgements

This work is partially supported by the Key Program of the National Natural Science Foundation of China (Grant No: 61836016); the Natural Science Foundation of China (Grants No: 61876046, 81701780, 61672177 and 61972177); the Project of Guangxi Science and Technology (GuiKeAD17195062); the Guangxi Natural Science Foundation (Grant No: 2017GXNSFBA198221); the Guangxi Collaborative Innovation Center of Multi-Source Information Integration and Intelligent Processing; the Research Fund of Guangxi Key Lab of Multisource Information Mining & Security (18-A-01-01); 2019 basic scientific research capability enhancement project for middle-aged teachers in guangxi university (2019KY0062); and Innovation Project of Guangxi Graduate Education (Grants No:YCSW20201008, JXXYYJSCXXM-008).

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Authors and Affiliations

  1. Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin, Guangxi, China

    Haiqi Zhang, Guangquan Lu, Mengmeng Zhan & Beixian Zhang

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  1. Haiqi Zhang
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Correspondence to Guangquan Lu.

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Zhang, H., Lu, G., Zhan, M. et al. Semi-Supervised Classification of Graph Convolutional Networks with Laplacian Rank Constraints. Neural Process Lett 54, 2645–2656 (2022). https://doi.org/10.1007/s11063-020-10404-7

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