Abstract
In this paper, we investigate whether graph kernels can be used as a means of analyzing time-varying financial market networks. Specifically, we aim to identify the significant financial incident that changes the financial network properties through graph kernels. Our financial networks are abstracted from the New York Stock Exchange (NYSE) data over 6004 trading days, where each vertex represents the individual daily return price time series of a stock and each edge represents the correlation between pairwise series. We propose to use two state-of-the-art graph kernels for the analysis, i.e., the Jensen-Shannon graph kernel and the Weisfeiler-Lehman subtree kernel. The reason of using the two kernels is that they are the representative methods of global graph kernels and local graph kernels, respectively. We perform kernel Principle Components Analysis (kPCA) associated with each kernel matrix to embed the networks into a 3-dimensional principle space, where the time-varying networks of all trading days are visualized. Experimental results on the financial time series of NYSE dataset demonstrate that graph kernels can well distinguish abrupt changes of financial networks with time, and provide a more effective alternative way of analyzing original multiple co-evolving financial time series. We theoretically indicate the perspective of developing novel graph kernels on time-varying networks for multiple co-evolving time series analysis in future work.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Anand, K., Bianconi, G., Severini, S.: Shannon and von neumann entropy of random networks with heterogeneous expected degree. Phys. Rev. E 83(3), 036109 (2011)
Anand, K., Krioukov, D., Bianconi, G.: Entropy distribution and condensation in random networks with a given degree distribution. Phys. Rev. E 89(6), 062807 (2014)
Bai, L., Hancock, E.R.: Graph kernels from the Jensen-Shannon divergence. J. Math. Imaging Vis. 47(1–2), 60–69 (2013)
Bai, L., Rossi, L., Torsello, A., Hancock, E.R.: A quantum Jensen-Shannon graph kernel for unattributed graphs. Pattern Recogn. 48(2), 344–355 (2015)
Bai, L., Rossi, L., Zhang, Z., Hancock, E.R.: An aligned subtree kernel for weighted graphs. In: Proceedings of ICML, pp. 30–39 (2015)
Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Proceedings of the IEEE International Conference on Data Mining, pp. 74–81 (2005)
Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)
Cuturi, M.: Fast global alignment kernels. In: Proceedings of ICML, pp. 929–936 (2011)
Dehmer, M., Mowshowitz, A.: A history of graph entropy measures. Inf. Sci. 181(1), 57–78 (2011)
Delvenne, J.-C., Libert, A.-S.: Centrality measures and thermodynamic formalism for complex networks. Phys. Rev. E 83(4), 046117 (2011)
Feldman, D.P., Crutchfield, J.P.: Measures of statistical complexity: why? Phys. Lett. A 238(4), 244–252 (1998)
Gärtner, T., Flach, P., Wrobel, S.: On graph kernels: hardness results and efficient alternatives. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT-Kernel 2003. LNCS (LNAI), vol. 2777, pp. 129–143. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45167-9_11
Huang, K.: Statistical Mechanic. Wiley, New York (1987)
Javarone, M.A., Armano, G.: Quantum-classical transitions in complex networks. J. Stat. Mech: Theory Exp. 2013(04), 04019 (2013)
Johansson, F.D., Jethava, V., Dubhashi, D.P., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: Proceedings of ICML, pp. 694–702 (2014)
Martins, A.F.T., Smith, N.A., Xing, E.P., Aguiar, P.M.Q., Figueiredo, M.A.T.: Nonextensive information theoretic kernels on measures. J. Mach. Learn. Res. 10, 935–975 (2009)
Nicolis, G., Cantu, A.G., Nicolis, C.: Dynamical aspects of interaction networks. Int. J. Bifurcat. Chaos 15, 3467 (2005)
Shervashidze, N., Vishwanathan, S.V.N., Mehlhorn, K., Petri, T., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. J. Mach. Learn. Res. 5, 488–495 (2009)
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)
Silva, F.N., Comin, C.H., Peron, T.K., Rodrigues, F.A., Ye, C., Wilson, R.C., Hancock, E.R., Costa, L.D.F.: Modular dynamics of financial market networks. arXiv preprint arXiv:1501.05040 (2015)
Witten, I.H., Frank, E., Hall, M.A.: Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann, Los Altos (2011)
Xu, L., Niu, X., Xie, J., Abel, A., Luo, B.: A local-global mixed kernel with reproducing property. Neurocomputing 168, 190–199 (2015)
Ye, C., Comin, C.H., Peron, T.K., Silva, F.N., Rodrigues, F.A., Costa, L.F., Torsello, A., Hancock, E.R.: Thermodynamic characterization of networks using graph polynomials. Phys. Rev. E 92(3), 032810 (2015)
Zhang, J., Small, M.: Complex network from pseudoperiodic time series: topology versus dynamics. Phys. Rev. Lett. 96, 238701 (2006)
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant no. 61602535, 61503422 and 61773415), the Open Projects Program of National Laboratory of Pattern Recognition, and the program for innovation research in Central University of Finance and Economics.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Cui, L., Bai, L., Rossi, L., Zhang, Z., Jiao, Y., Hancock, E.R. (2018). A Preliminary Survey of Analyzing Dynamic Time-Varying Financial Networks Using Graph Kernels. In: Bai, X., Hancock, E., Ho, T., Wilson, R., Biggio, B., Robles-Kelly, A. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2018. Lecture Notes in Computer Science(), vol 11004. Springer, Cham. https://doi.org/10.1007/978-3-319-97785-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-97785-0_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97784-3
Online ISBN: 978-3-319-97785-0
eBook Packages: Computer ScienceComputer Science (R0)