Abstract
We solve the problem of classification on graphs by generating a similarity matrix from a graph with virtual edges created using predefined rules. The rules are defined based on axioms for similarity spaces. Virtual edges are generated by solving the problem of computing paths with maximal fixed length. We perform experiments by using the similarity matrix as a kernel matrix in support vector machines (SVM). We consider two versions of SVM: for inductive and transductive learning. The experiments show that virtual edges reduce the number of support vectors. When comparing to kernels on graphs, the SVM method with virtual edges is faster while preserving similar generalization performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Borgwardt, K.M., Kriegel, H.: Shortest-path kernels on graphs. In: Proceedings of the 5th IEEE International Conference on Data Mining (ICDM 2005), Houston, Texas, USA, 27–30 November 2005, pp. 74–81 (2005). https://doi.org/10.1109/ICDM.2005.132
Bronshtein, I.N., Semendyayev, K., Musiol, G., Muehlig, H.: Handbook of Mathematics. In: Functional Analysis, pp. 596–641. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72122-2_12
Can, T., Çamoglu, O., Singh, A.K.: Analysis of protein-protein interaction networks using random walks. In: Proceedings of the 5th International Workshop on Bioinformatics, BIOKDD 2005, Chicago, Illinois, USA, 21 August 2005, pp. 61–68 (2005). https://doi.org/10.1145/1134030.1134042
Chen, Y., Garcia, E.K., Gupta, M.R., Rahimi, A., Cazzanti, L.: Similarity-based classification: concepts and algorithms. J. Mach. Learn. Res. 10, 747–776 (2009)
Fouss, F., Françoisse, K., Yen, L., Pirotte, A., Saerens, M.: An experimental investigation of kernels on graphs for collaborative recommendation and semisupervised classification. Neural Netw. 31, 53–72 (2012). https://doi.org/10.1016/j.neunet.2012.03.001
Gallagher, B., Tong, H., Eliassi-Rad, T., Faloutsos, C.: Using ghost edges for classification in sparsely labeled networks. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Las Vegas, Nevada, USA, 24–27 August 2008, pp. 256–264 (2008). https://doi.org/10.1145/1401890.1401925
Kondor, R., Lafferty, J.D.: Diffusion kernels on graphs and other discrete input spaces. In: Machine Learning, Proceedings of the Nineteenth International Conference (ICML 2002), Sydney, Australia, 8–12 July 2002, pp. 315–322, University of New South Wales (2002)
LIBSVM Data Sets, July 2011. www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/
Lin, F., Cohen, W.W.: Semi-supervised classification of network data using very few labels. In: International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2010, Odense, Denmark, 9–11 August 2010, pp. 192–199 (2010). https://doi.org/10.1109/ASONAM.2010.19
Melki, G., Kecman, V., Ventura, S., Cano, A.: OLLAWV: online learning algorithm using worst-violators. Appl. Soft Comput. 66, 384–393 (2018)
Namata, G., Sen, P., Bilgic, M., Getoor, L.: Collective classification. In: Sammut, C., Webb, G.I. (eds.) Encyclopedia of Machine Learning and Data Mining, pp. 238–242. Springer, Boston (2017). https://doi.org/10.1007/978-1-4899-7687-1_44
Pan, S., Zhu, X., Zhang, C., Yu, P.S.: Graph stream classification using labeled and unlabeled graphs. In: 29th IEEE International Conference on Data Engineering, ICDE 2013, Brisbane, Australia, 8–12 April 2013, pp. 398–409 (2013). https://doi.org/10.1109/ICDE.2013.6544842
Perozzi, B., Al-Rfou, R., Skiena, S.: DeepWalk: online learning of social representations. In: The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2014, New York, NY, USA, 24–27 August 2014, pp. 701–710 (2014). https://doi.org/10.1145/2623330.2623732
Schölkopf, B., Tsuda, K., Vert, J.P.: Kernel methods in computational biology. In: Diffusion Kernels, pp. 171–192, 16 July 2004. The MIT Press, January 2003
Shervashidze, N., Schweitzer, P., van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. J. Mach. Learn. Res. 12, 2539–2561 (2011)
Smola, A.J., Kondor, R.: Kernels and regularization on graphs. In: Computational Learning Theory and Kernel Machines, Proceedings of the 16th Annual Conference on Computational Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, 24–27 August 2003, pp. 144–158 (2003)
Vapnik, V.N.: Statistical Learning Theory. Wiley-Interscience (1998)
Vorontsov, K., Ivahnenko, A.: Tight combinatorial generalization bounds for threshold conjunction rules. In: Kuznetsov, S.O., Mandal, D.P., Kundu, M.K., Pal, S.K. (eds.) PReMI 2011. LNCS, vol. 6744, pp. 66–73. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21786-9_13
Wu, G., Chang, E.Y., Zhang, Z.: An analysis of transformation on non-positive semidefinite similarity matrix for kernel machines. In: Proceedings of the 22nd International Conference on Machine Learning (2005)
Yajima, Y., Kuo, T.: Efficient formulations for 1-SVM and their application to recommendation tasks. JCP 1(3), 27–34 (2006). https://doi.org/10.4304/jcp.1.3.27-34
Acknowledgments
The theoretical analysis and the method design are financed by the National Science Centre in Poland, project id 289884, UMO-2015/17/D/ST6/04010, titled “Development of Models and Methods for Incorporating Knowledge to Support Vector Machines” and the data driven method is supported by the European Research Council under the European Union’s Seventh Framework Programme. Johan Suykens acknowledges support by ERC Advanced Grant E-DUALITY (787960), KU Leuven C1, FWO G0A4917N. This paper reflects only the authors’ views, the Union is not liable for any use that may be made of the contained information.
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
Orchel, M., Suykens, J.A.K. (2019). Axiomatic Kernels on Graphs for Support Vector Machines. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Workshop and Special Sessions. ICANN 2019. Lecture Notes in Computer Science(), vol 11731. Springer, Cham. https://doi.org/10.1007/978-3-030-30493-5_62
Download citation
DOI: https://doi.org/10.1007/978-3-030-30493-5_62
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30492-8
Online ISBN: 978-3-030-30493-5
eBook Packages: Computer ScienceComputer Science (R0)