Abstract
Riesen and Bunke recently proposed a novel dissimilarity based approach for embedding graphs into a vector space. One drawback of their approach is the computational cost graph edit operations required to compute the dissimilarity for graphs. In this paper we explore whether the Jensen-Shannon divergence can be used as a means of computing a fast similarity measure between a pair of graphs. We commence by computing the Shannon entropy of a graph associated with a steady state random walk. We establish a family of prototype graphs by using an information theoretic approach to construct generative graph prototypes. With the required graph entropies and a family of prototype graphs to hand, the Jensen-Shannon divergence between a sample graph and a prototype graph can be computed. It is defined as the Jensen-Shannon between the pair of separate graphs and a composite structure formed by the pair of graphs. The required entropies of the graphs can be efficiently computed, the proposed graph embedding using the Jensen-Shannon divergence avoids the burdensome graph edit operation. We explore our approach on several graph datasets abstracted from computer vision and bioinformatics databases.
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Bai, L., Hancock, E.R., Han, L. (2013). A Graph Embedding Method Using the Jensen-Shannon Divergence. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds) Computer Analysis of Images and Patterns. CAIP 2013. Lecture Notes in Computer Science, vol 8047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40261-6_12
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DOI: https://doi.org/10.1007/978-3-642-40261-6_12
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