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Flexible data representation with graph convolution for semi-supervised learning

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Abstract

This paper introduces a scheme for semi-supervised data representation. It proposes a flexible nonlinear embedding model that imitates the principle of spectral graph convolutions. Structured data are exploited in order to determine nonlinear and linear models. The introduced scheme takes advantage of data graphs at two different levels. First, it incorporates manifold regularization that is naturally encoded by the graph itself. Second, the regression model is built on the convolved data samples that are obtained by the joint use of the data and their associated graph. The proposed semi-supervised embedding can tackle challenges related to over-fitting in image data spaces. The proposed graph convolution-based semi-supervised embedding paves the way to new theoretical and application perspectives related to the nonlinear embedding. Indeed, building flexible models that adopt convolved data samples can enhance both the data representation and the final performance of the learning system. Several experiments are conducted on six image datasets for comparing the introduced scheme with many state-of-art semi-supervised approaches. These experimental results show the effectiveness of the introduced data representation scheme.

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Notes

  1. http://www.cs.nyu.edu/~roweis/data.html.

  2. www.facepix.org/.

References

  1. Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434

    MathSciNet  MATH  Google Scholar 

  2. Belkin M, Niyogi P (2001) Laplacian eigenmaps and spectral techniques for embedding and clustering. Adv Neural Inform Process Syst 14:585–591

    Google Scholar 

  3. Cai D, He X, Han J (2007) Semi-supervised discriminant analysis. In: IEEE international conference on computer vision, pp 1–7

  4. Dornaika F, El Traboulsi Y (2016) Learning flexible graph-based semi-supervised embedding. IEEE Trans Cybern 46(1):206–218

    Article  Google Scholar 

  5. Dornaika F, Traboulsi YE (2017) Matrix exponential based semi-supervised discriminant embedding. Pattern Recognit 61:92–103

    Article  Google Scholar 

  6. Dornaika F, Traboulsi YE (2019) Joint sparse graph and flexible embedding for graph-based semi-supervised learning. Neural Netw 114:91–95

    Article  Google Scholar 

  7. Dornaika F, Kejani M, Bosaghzadeh A (2017) Graph construction using adaptive local hybrid coding scheme. Neural Netw 95:91–101

    Article  Google Scholar 

  8. El Traboulsi Y, Dornaika F, Assoum A (2015) Kernel flexible manifold embedding for pattern classification. Neurocomputing 167:517–527

    Article  Google Scholar 

  9. Fang X, Xu Y, Li X, Lai Z, Wong WK (2015) Learning a nonnegative sparse graph for linear regression

  10. Franceschi L, Niepert M, Pontil M, He X (2019) Learning discrete structures for graph neural networks. In: International conference on machine learning, pp 1972–1982

  11. Hamilton ZYW, Leskovec J (2017) Inductive representation learning on large graphs. In: Advances in neural information processing systems, pp 1024–1034

  12. Hou C, Nie F, Li X, Yi D, Wu Y (2014) Joint embedding learning and sparse regression: a framework for unsupervised feature selection. IEEE Trans Cybern 44(6):793–804

    Article  Google Scholar 

  13. Huang H, Liu J, Pan Y (2012) Semi-supervised marginal fisher analysis for hyperspectral image classification. ISPRS Ann Photogramm Remote Sens Spatial Inform Sci 3:377–382

    Article  Google Scholar 

  14. Kar P, Li S, Narasimhan H, Chawla S, Sebastiani F (2016)Online optimization methods for the quantification problem. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining

  15. Kejani MT, Dornaika F, Talebi H (2020) Graph convolution networks with manifold regularization for semi-supervised learning. Neural Netw 127:160–167

    Article  Google Scholar 

  16. Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. In: International conference on learning representations

  17. Klicpera ABJ, Gunnemann S (2019) Predict then propagate: graph neural networks meet personalized pagerank. In: International conference on learning representations

  18. Korda N, Szorenyi, B, Li S (2016) Distributed clustering of linear bandits in peer to peer networks. In: International conference on machine learning

  19. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems, pp 1097–1105

  20. Lazebnik S, Schmid C, Ponce J (2006) Beyond bags of features: spatial pyramid matching for recognizing natural scene categories. In: IEEE conference on computer vision and pattern recognition, pp 2169–2178

  21. 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 

  22. Li LJ, Li FF (2007) What, where and who? Classifying events by scene and object recognition. In: IEEE international conference on computer vision, pp 1–8

  23. Liang Y, You L, Lu X, He Z, Wang H (2018) Low-rank projection learning via graph embedding. Neurocomputing 348:97–106

    Article  Google Scholar 

  24. Li S, Chen W, Li S, Leung K-S (2019) Improved algorithm on online clustering of bandits. arXiv:1902.09162

  25. Li S, Karatzoglou A, Gentile C (2016) Collaborative filtering bandits. arXiv:1502.03473

  26. Liu W, Wang J, Chang S-F (2012) Graph-based semi-supervised learning. Proc IEEE 100(9):2624–2638

    Article  Google Scholar 

  27. Liu W, Chang S-F (2009) Robust multi-class transductive learning with graphs. In: IEEE conference on computer vision and pattern recognition, 2009. CVPR 2009, pp 381–388. IEEE

  28. Mahadik K, Wu Q, Li S, Sabne A (2020) Fast distributed bandits for online recommendation systems

  29. Nene SA, Nayar S, Murase H (1996) Columbia object image library (COIL-20). In: Technical report CUCS-005-96

  30. Nie F, Xu D, Tsang IW-H, Zhang C (2010) Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction. IEEE Trans Image Process 19(7):1921–1932

    Article  MathSciNet  Google Scholar 

  31. Nie F, Wang Z, Wang R, Li X (2020) Submanifold-preserving discriminant analysis with an auto-optimized graph. IEEE Trans Cybern 50(8):3682–3695

    Article  Google Scholar 

  32. Nie F, Cai G, Li X (2017) Multi-view clustering and semi-supervised classification with adaptive neighbours. In: Thirty-first AAAI conference on artificial intelligence, pp 1501–1511

  33. Nie F, Dong F, Li X (2020) Unsupervised and semisupervised projection with graph optimization. In: IEEE transactions on neural networks and learning systems

  34. Ojala T, Pietikäinen M, Harwood D (1996) A comparative study of texture measures with classification based on featured distributions. Pattern Recognit 29(1):51–59

    Article  Google Scholar 

  35. Qiao L, Chen S, Tan X (2010) Sparsity preserving discriminant analysis for single training image face recognition. Pattern Recognit Lett 31(5):422–429

    Article  Google Scholar 

  36. Qu M, Bengio Y, Tang J (2019) GMNN: graph Markov neural networks. In: International conference on machine learning, pp 5241–5250

  37. Raducanu B, Dornaika F (2012) A supervised non-linear dimensionality reduction approach for manifold learning. Pattern Recognit 45(6):2432–2444

    Article  Google Scholar 

  38. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Article  Google Scholar 

  39. Tenenbaum JB, De Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  40. Velickovic WL H P L YB P, Fedus W, Hjelm RD (2019) Deep graph infomax. In: International conference on learning representations

  41. Wan M, Li M, Yang G, Gai S, Jin Z (2014) Feature extraction using two-dimensional maximum embedding difference. Inf Sci 274:55–69

    Article  Google Scholar 

  42. Wan M, Lai Z, Yang G, Yang Z, Zhang F, Zheng H (2017) Local graph embedding based on maximum margin criterion via fuzzy set. Fuzzy Sets Syst 318:120–131

    Article  MathSciNet  Google Scholar 

  43. Wang F, Wang X, Zhang D, Zhang C, Li T (2009) Marginface: a novel face recognition method by average neighborhood margin maximization. Pattern Recognit 42(11):2863–2875

    Article  Google Scholar 

  44. Wang H, Leskovec J (2020) Unifying graph convolutional neural networks and label propagation. arXiv preprint arXiv:2002.06755

  45. Wen J, Xu Y, Liu H (2020) Incomplete multiview spectral clustering with adaptive graph learning. IEEE Trans Cybern 50(4):1418–1429

    Article  Google Scholar 

  46. Wu H, Prasad S (2018) Semi-supervised dimensionality reduction of hyperspectral imagery using pseudo-labels. Pattern Recognit 74:212–224

    Article  Google Scholar 

  47. Wu F, Souza A, Zhang T, Fifty C, Yu T, Weinberger K (2019) Simplifying graph convolutional networks. In: International conference on machine learning, pp 6861–6871

  48. Yan S, Xu D, Zhang B, Zhang H, Yang Q, Lin S (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40–51

    Article  Google Scholar 

  49. Yu G, Zhang G, Domeniconi C, Yu Z, You J (2012) Semi-supervised classification based on random subspace dimensionality reduction. Pattern Recognit 45(3):1119–1135

    Article  Google Scholar 

  50. Yuan Y, Mou L, Lu X (2015) Scene recognition by manifold regularized deep learning architecture. IEEE Trans Neural Netw Learn Syst 26(10):2222–2233

    Article  MathSciNet  Google Scholar 

  51. Zhang Z, Jia L, Zhao M, Ye Q, Zhang M, Wang M (2018) Adaptive non-negative projective semi-supervised learning for inductive classification. Neural Netw 108:128–145

    Article  Google Scholar 

  52. Zhao M, Zhang Y, Zhang Z, Liu J, Kong W (2019) Alg: Adaptive low-rank graph regularization for scalable semi-supervised and unsupervised learning. Neurocomputing 370:16–27

    Article  Google Scholar 

  53. Zhu R, Dornaika F, Ruichek Y (2019) Joint graph based embedding and feature weighting for image classification. Pattern Recognit 93:458–469

    Article  Google Scholar 

  54. Zhu R, Dornaika F, Ruichek Y (2019) Learning a discriminant graph-based embedding with feature selection for image categorization. Neural Netw 111:35–46

    Article  Google Scholar 

  55. Zhu R, Dornaika F, Ruichek Y (2020) Semi-supervised elastic manifold embedding with deep learning architecture. Pattern Recognit 107:107425

    Article  Google Scholar 

  56. Zhu X, Ghahramani Z, Lafferty J et al (2003) Semi-supervised learning using Gaussian fields and harmonic functions, vol 3, pp 912–919

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Authors and Affiliations

  1. University of the Basque Country (UPV/EHU), San Sebastián, Spain

    Fadi Dornaika

  2. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    Fadi Dornaika

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  1. Fadi Dornaika
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Correspondence to Fadi Dornaika.

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Dornaika, F. Flexible data representation with graph convolution for semi-supervised learning. Neural Comput & Applic 33, 6851–6863 (2021). https://doi.org/10.1007/s00521-020-05462-w

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