Abstract
In this paper we aim to characterize graphs in terms of structural complexities. Our idea is to decompose a graph into substructures of increasing layers, and then to measure the dissimilarity of these substructures using Jensen-Shannon divergence. We commence by identifying a centroid vertex by computing the minimum variance of its shortest path lengths. From the centroid vertex, a family of centroid expansion subgraphs of the graph with increasing layers are constructed. We then compute the depth-based complexity trace of a graph by measuring how the Jensen-Shannon divergence varies with increasing layers of the subgraphs. The required Shannon or von Neumann entropies are computed on the condensed subgraph family of the graph. We perform graph clustering in the principal components space of the complexity trace vector. Experiments on graph datasets abstracted from bioinformatics and image data demonstrate effectiveness and efficiency of the graphs complexity traces.
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References
Crutchfield, J.P., Shalizi, C.R.: Thermodynamic depth of causal states: Objective complexity via minimal representations. Physical Review E 59, 275–283 (1999)
Escolano, F., Hancock, E.R., Lozano, M.A.: Heat diffusion: Thermodynamic depth complexity of networks. Physical Review E 85, 206–236 (2012)
Han, L., Escolano, F., Hancock, E.R.: Graph characterizations from von Neumann entropy. To appear in Pattern Recognition Letter (2012)
Martins, A.F.T., Smith, N.A., Xing, E.P., Aguiar, P.M.Q., Figueiredo, M.A.T.: Nonextensive information theoretic kernels on measures. Journal of Machine Learning Research 10, 935–975 (2009)
Bunke, H., Riesen, K.: Improving vector space embedding of graphs through feature selection algorithms. Pattern Recognition 44, 1928–1940 (2011)
Bai, L., Hancock, E.R.: Graph Clustering Using the Jensen-Shannon Kernel. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds.) CAIP 2011, Part I. LNCS, vol. 6854, pp. 394–401. Springer, Heidelberg (2011)
Ren, P., Wilson, R.C., Hancock, E.R.: Graph Characterization via Ihara Coefficients. IEEE Transactions on Neural Networks 22, 233–245 (2011)
Dehmer, M., Mowshowitz, A.: A history of graph entropy measures. Proceedings of Information Sciences 181, 57–78 (2011)
Shervashidze, N., Schweitzer, P., Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. Journal of Machine Learning Research 1, 1–48 (2010)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Transactions Pattern Analysis and Machine Intelligence 27, 1112–1124 (2005)
Han, L., Hancock, E.R., Wilson, R.C.: Learning Generative Graph Prototypes Using Simplified von Neumann Entropy. In: Jiang, X., Ferrer, M., Torsello, A. (eds.) GbRPR 2011. LNCS, vol. 6658, pp. 42–51. Springer, Heidelberg (2011)
Passerini, F., Severini, S.: Quantifying complexity in networks: the von Neumann entropy. International Journal of Agent Technologies and Systems 1, 58–67 (2009)
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Bai, L., Hancock, E.R. (2012). Graph Complexity from the Jensen-Shannon Divergence. In: Gimel’farb, G., et al. Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2012. Lecture Notes in Computer Science, vol 7626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34166-3_9
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DOI: https://doi.org/10.1007/978-3-642-34166-3_9
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