Abstract
Many learning problems can be cast into learning from data-driven graphs. This paper introduces a framework for supervised and semi-supervised learning by estimating a non-linear embedding that incorporates Spectral Graph Convolutions structure. The proposed algorithm exploits data-driven graphs in two ways. First, it integrates data smoothness over graphs. Second, the regression is solved by the joint use of the data and their graph in the sense that the regressor sees convolved data samples. The resulting framework can solve the problem of over-fitting on local neighborhood structures for image data having varied natures like outdoor scenes, faces and man-made objects. Our proposed approach not only provides a new perspective to non-linear embedding research but also induces the standpoint on Spectral Graph Convolutions methods. In order to evaluate the performance of the proposed method, a series of experiments are conducted on four image datasets in order to compare the proposed method with some state-of-art algorithms. This evaluation demonstrates the effectiveness of the proposed embedding method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, pp. 585–591 (2002)
Cai, D., He, X., Han, J.: Semi-supervised discriminant analysis. In: 2007 IEEE 11th International Conference on Computer Vision, pp. 1–7 (2007)
Chen, H.T., Chang, H.W., Liu, T.L.: Local discriminant embedding and its variants. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 2, pp. 846–853. IEEE (2005)
Dornaika, F., El Traboulsi, Y.: Learning flexible graph-based semi-supervised embedding. IEEE Trans. Cybern. 46(1), 206–218 (2016)
El Traboulsi, Y., Dornaika, F., Assoum, A.: Kernel flexible manifold embedding for pattern classification. Neurocomputing 167, 517–527 (2015)
Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)
Hou, C., Nie, F., Li, X., Yi, D., Wu, Y.: Joint embedding learning and sparse regression: a framework for unsupervised feature selection. IEEE Trans. Cybern. 44(6), 793–804 (2014)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: International Conference on Learning Representations (2017)
Kong, D., Ding, C.H.Q., Huang, H., Nie, F.: An iterative locally linear embedding algorithm. In: International Conference on Machine Learning, pp. 1647–1654 (2012)
Lazebnik, S., Schmid, C., Ponce, J.: Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2006, vol. 2, pp. 2169–2178. IEEE (2006)
Li, L.J., Fei-Fei, L.: What, where and who? classifying events by scene and object recognition. In: IEEE 11th International Conference on Computer Vision, ICCV 2007, pp. 1–8. IEEE (2007)
MartÃnez, A.M., Kak, A.C.: pCA versus LDA. IEEE Trans. Pattern Anal. Mach. Intell. 23(2), 228–233 (2001)
Nene, S.A., Nayar, S., Murase, H.: Columbia object image library (coil-20). Technical report CUCS-005-96 (1996)
Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 29(1), 51–59 (1996)
Raducanu, B., Dornaika, F.: A supervised non-linear dimensionality reduction approach for manifold learning. Pattern Recogn. 45(6), 2432–2444 (2012)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Yu, G., Zhang, G., Domeniconi, C., Yu, Z., You, J.: Semi-supervised classification based on random subspace dimensionality reduction. Pattern Recogn. 45(3), 1119–1135 (2012)
Yuan, Y., Mou, L., Lu, X.: Scene recognition by manifold regularized deep learning architecture. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2222–2233 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Zhu, R., Dornaika, F., Ruichek, Y. (2019). Discriminant Manifold Learning with Graph Convolution Based Regression for Image Classification. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-20081-7_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20080-0
Online ISBN: 978-3-030-20081-7
eBook Packages: Computer ScienceComputer Science (R0)