Information Theoretic Prototype Selection for Unattributed Graphs
Conference paper
Abstract
In this paper we propose a prototype size selection method for a set of sample graphs. Our first contribution is to show how approximate set coding can be extended from the vector to graph domain. With this framework to hand we show how prototype selection can be posed as optimizing the mutual information between two partitioned sets of sample graphs. We show how the resulting method can be used for prototype graph size selection. In our experiments, we apply our method to a real-world dataset and investigate its performance on prototype size selection tasks.
Keywords
Prototype Selection Mutual information Importance Sampling Partition function Download
to read the full conference paper text
References
- 1.Han, L., Wilson, R.C., Hancock, E.R.: A Supergraph-based Generative Model. In: ICPR, pp. 1566–1569 (2010)Google Scholar
- 2.Torsello, A.: An Importance Sampling Approach to Learning Structural Representations of Shape. In: CVPR, pp. 1–7 (2008)Google Scholar
- 3.Buhmann, J.M., Chehreghani, M.H., Frank, M., Streich, A.P.: Information Theoretic Model Selection for Pattern Analysis. JMLR: Workshop and Conference Proceedings 7, 1–15 (2011)Google Scholar
- 4.Buhmann, J.M.: Information Thereotic Model Validation for Clustering. In: International Symposium on Information Theory, pp. 1398–1402 (2010)Google Scholar
- 5.Nene, S.A., Nayar, S.K., Murase, H.: Columbia Object Image Library(COIL100). Columbia University (1996)Google Scholar
- 6.National Center for Biotechnology Information, http://www.ncbi.nlm.nih.gov
- 7.Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods. Wiley, New York (1964)zbMATHCrossRefGoogle Scholar
- 8.Han, L., Hancock, E.R., Wilson, R.C.: Learning Generative Graph Prototypes Using Simplified von Neumann Entropy. In: GbRPR, p. 4251 (2011)Google Scholar
- 9.Rissanen, J.: Modelling by Shortest Data Description. Automatica 14, 465–471 (1978)zbMATHCrossRefGoogle Scholar
- 10.Schwarz, G.E.: Estimating the dimension of a model. Annals of Statistics 6, 461–464 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
- 11.Foster, D.P., George, E.I.: The Risk Inflation Criterion for Multiple Regression. Annals of Statistics 22, 1947–1975 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
- 12.White, D., Wilson, R.C.: Parts based generative models for graphs. In: ICPR, pp. 1–4 (2008)Google Scholar
- 13.Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
- 14.Grnwald, P.D., Myung, I.J., Pitt, M.A.: Advances in Minimum Description Length: Theory and Applications. The MIT Press (2005)Google Scholar
- 15.Luo, B., Hancock, E.R.: Structural graph matching using the EM alogrithm and singular value decomposition. IEEE Transactions on PAMI 23, 1120–1136 (2001)CrossRefGoogle Scholar
- 16.Sinkhorn, R.: A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices. The Annals of Mathematical Statistics 35, 876–879 (1964)MathSciNetzbMATHCrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2012