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An Algorithm for Directed Graph Estimation

  • Hideitsu Hino
  • Atsushi Noda
  • Masami Tatsuno
  • Shotaro Akaho
  • Noboru Murata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8681)

Abstract

A problem of estimating the intrinsic graph structure from observed data is considered. The observed data in this study is a matrix with elements representing dependency between nodes in the graph. Each element of the observed matrix represents, for example, co-occurrence of events at two nodes, or correlation of variables corresponding to two nodes. The dependency does not represent direct connections and includes influences of various paths, and spurious correlations make the estimation of direct connection difficult. To alleviate this difficulty, digraph Laplacian is used for characterizing a graph. A generative model of an observed matrix is proposed, and a parameter estimation algorithm for the model is also proposed. The proposed method is capable of dealing with directed graphs, while conventional graph structure estimation methods from an observed matrix are only applicable to undirected graphs. Experimental result shows that the proposed algorithm is able to identify the intrinsic graph structure.

Keywords

digraph Laplacian directed graph graph estimation 

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References

  1. 1.
    Bunke, H., Riesen, K.: Recent advances in graph-based pattern recognition with applications in document analysis. Pattern Recognition 44(5), 1057–1067 (2011)CrossRefzbMATHGoogle Scholar
  2. 2.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2003)CrossRefGoogle Scholar
  3. 3.
    Page, L., Brin, S., Motowani, R., Winograd, T.: PageRank citation ranking: Bring order to the web. Stanford Digital Library Working Paper (1997)Google Scholar
  4. 4.
    Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2007)CrossRefGoogle Scholar
  5. 5.
    Dempster, A.: Covariance selection. Biometrics 28, 157–175 (1972)CrossRefGoogle Scholar
  6. 6.
    Li, Y., Zhang, Z.-L.: Random Walks on Digraphs, the Generalized Digraph Laplacian and the Degree of Asymmetry. In: Kumar, R., Sivakumar, D. (eds.) WAW 2010. LNCS, vol. 6516, pp. 74–85. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Higham, N.J.: Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia (2008)CrossRefGoogle Scholar
  8. 8.
    Lagarias, J., Reeds, J., Wright, M., Wright, P.: Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal on Optimization 9(1), 112–147 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Tatsuno, M., Lipa, P., McNaughton, B.L.: Methodological considerations on the use of template matching to study long-lasting memory trace replay. Journal of Neuroscience 26(42), 10727–10742 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hideitsu Hino
    • 1
  • Atsushi Noda
    • 2
  • Masami Tatsuno
    • 3
  • Shotaro Akaho
    • 4
  • Noboru Murata
    • 2
  1. 1.University of TsukubaTsukubaJapan
  2. 2.Waseda UniversityShinjuku-kuJapan
  3. 3.University of LethbridgeLethbridgeCanada
  4. 4.National Institute of Advanced Industrial Science and TechnologyTsukubaJapan

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