Generative Graph Prototypes from Information Theory

IEEE Transactions on Pattern Analysis and Machine Intelligence
Lin HanEdwin R Hancock

Abstract

In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs.

References

Oct 16, 1999·Science·A L Barabasi, R Albert
May 14, 2003·Proceedings of the National Academy of Sciences of the United States of America·Fan ChungVan Vu
May 27, 2006·IEEE Transactions on Pattern Analysis and Machine Intelligence·Andrea Torsello, Edwin R Hancock
Jun 13, 2006·Neural Computation·Geoffrey E HintonYee-Whye Teh
Dec 2, 2010·IEEE Transactions on Neural Networks·Peng RenEdwin R Hancock
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kartik AnandSimone Severini

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