Global graph kernels using geometric embeddings

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Fredrik Johansson, Vinay Jethava, Devdatt Dubhashi, Chiranjib Bhattacharyya ;
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):694-702, 2014.

Abstract

Applications of machine learning methods increasingly deal with graph structured data through kernels. Most existing graph kernels compare graphs in terms of features defined on small subgraphs such as walks, paths or graphlets, adopting an inherently local perspective. However, several interesting properties such as girth or chromatic number are global properties of the graph, and are not captured in local substructures. This paper presents two graph kernels defined on unlabeled graphs which capture global properties of graphs using the celebrated Lovász number and its associated orthonormal representation. We make progress towards theoretical results aiding kernel choice, proving a result about the separation margin of our kernel for classes of graphs. We give empirical results on classification of synthesized graphs with important global properties as well as established benchmark graph datasets, showing that the accuracy of our kernels is better than or competitive to existing graph kernels.

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