Abstract
In this paper, we propose an embedding method for attributed graphs. For an attributed graph, we commence by using a tree-index method with the objective of strengthening the vertex labels. For each iteration of the tree-index method, we compute a probability distribution in terms of the frequency of the strengthened labels. With each probability distribution, we compute a Shannon entropy to measure the uncertainty of the strengthened labels. For an attributed graph, with the required Shannon entropies of different TI iterations to hand, we compute an entropy trace vector by measuring how the entropies vary with the increasing TI iterations (i.e., we embed the attributed graph into a vectorial space). We explore our method on several standard graph datasets abstracted from bioinformatics databases. The experimental results demonstrate the effectiveness and efficiency of our method. Our method can easily outperform state of the art methods in terms of the classification accuracy.
Y. Jiao and Y. Yang—Equally contributed.
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References
Bai, L., Hancock, E.R.: Depth-based complexity traces of graphs. Pattern Recognit. 47(3), 1172–1186 (2014)
Bai, L., Hancock, E.R., Han, L.: A graph embedding method using the Jensen-Shannon divergence. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds.) CAIP 2013. LNCS, vol. 8047, pp. 102–109. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40261-6_12
Bai, L., Rossi, L., Bunke, H., Hancock, E.R.: Attributed graph kernels using the Jensen-Tsallis q-differences. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds.) ECML PKDD 2014, Part I. LNCS (LNAI), vol. 8724, pp. 99–114. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44848-9_7
Dahm, N., Bunke, H., Caelli, T., Gao, Y.: A unified framework for strengthening topological node features and its application to subgraph isomorphism detection. In: Kropatsch, W.G., Artner, N.M., Haxhimusa, Y., Jiang, X. (eds.) GbRPR 2013. LNCS, vol. 7877, pp. 11–20. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38221-5_2
Dehmer, M.: Information processing in complex networks: graph entropy and information functionals. Appl. Math. Comput. 201(1–2), 82–94 (2008)
Dehmer, M., Mowshowitz, A.: A history of graph entropy measures. Inf. Sci. 181(1), 57–78 (2011)
Escolano, F., Bonev, B., Hancock, E.R.: Heat flow-thermodynamic depth complexity in directed networks. In: Gimel’farb, G., et al. (eds.) SSPR /SPR 2012. LNCS, vol. 7626, pp. 190–198. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34166-3_21
Han, L., Escolano, F., Hancock, E.R., Wilson, R.C.: Graph characterizations from von Neumann entropy. Pattern Recognit. Lett. 33(15), 1958–1967 (2012)
Maimon, O., Rokach, L. (eds.): Data Mining and Knowledge Discovery Handbook, 2nd edn. Springer, Boston (2010). https://doi.org/10.1007/978-0-387-09823-4
Ren, P., Wilson, R.C., Hancock, E.R.: Graph characterization via Ihara coefficients. IEEE Trans. Neural Netw. 22(2), 233–245 (2011)
Riesen, K., Bunke, H.: Reducing the dimensionality of dissimilarity space embedding graph kernels. Eng. Appl. Artif. Intell. 22(1), 48–56 (2009)
Vishwanathan, S.V.N., Sun, Z., Ampornpunt, N., Varma, M.: Multiple kernel learning and the SMO algorithm. In: NIPS, pp. 2361–2369 (2010)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1112–1124 (2005)
Xu, L., Jiang, X., Bai, L., Xiao, J., Luo, B.: A hybrid reproducing graph kernel based on information entropy. Pattern Recognit. 73, 89–98 (2018)
Acknowledgments
This work is supported by National Key R&D Program of China (No. 2017YFB1400700), the National Natural Science Foundation of China (Grant no. 61602535 and 61503422), the Open Projects Program of National Laboratory of Pattern Recognition (NLPR), the Graduate Research Innovation Fund of Central University of Finance and Economics (No. 20181Y019), and the program for innovation research in Central University of Finance and Economics.
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Jiao, Y., Yang, Y., Cui, L., Bai, L. (2019). An Attributed Graph Embedding Method Using the Tree-Index Algorithm. 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_17
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