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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bunke, H., Riesen, K.: Recent advances in graph-based pattern recognition with applications in document analysis. Pattern Recognition 44(5), 1057–1067 (2011)
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)
Page, L., Brin, S., Motowani, R., Winograd, T.: PageRank citation ranking: Bring order to the web. Stanford Digital Library Working Paper (1997)
Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2007)
Dempster, A.: Covariance selection. Biometrics 28, 157–175 (1972)
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)
Higham, N.J.: Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia (2008)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Hino, H., Noda, A., Tatsuno, M., Akaho, S., Murata, N. (2014). An Algorithm for Directed Graph Estimation. In: Wermter, S., et al. Artificial Neural Networks and Machine Learning – ICANN 2014. ICANN 2014. Lecture Notes in Computer Science, vol 8681. Springer, Cham. https://doi.org/10.1007/978-3-319-11179-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-11179-7_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11178-0
Online ISBN: 978-3-319-11179-7
eBook Packages: Computer ScienceComputer Science (R0)