Evaluating graph generative models with graph kernels: what structural characteristics are captured?

Martijn Gösgens, Alexey Tikhonov, Liudmila Prokhorenkova

Primary Area: general machine learning (i.e., none of the above)

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Keywords: graph kernel, random graph model, degree distribution, community structure, graph generative model

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Abstract:

For a number of practical problems, it is important to measure the similarity between graphs. In particular, it is essential for assessing the quality of graph generative models. In evaluation measures for graph generative models, graph kernels are often used to measure the similarity of graphs. Recently, it has been shown that the choice of a graph kernel may drastically affect research outcomes in this area. Therefore, it is essential to choose a kernel that is suitable for the task at hand. In this paper, we propose a framework for comparing graph kernels in terms of which high-level structural properties they are sensitive to. For this, we choose several pairs of random graph models that are different in one particular property: heterogeneity of degree distribution, the presence of community structure, the presence or particular type of latent geometry, and others. Then, we design continuous transitions between these models and measure which graph kernel is sensitive to the corresponding change. We show that using such diverse graph modifications is crucial for evaluation: many kernels can successfully capture some properties and fail on others. One of our conclusions is that simple and long-known Shortest Path and Graphlet kernels are able to successfully capture all graph properties that we consider in this work.

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Submission Number: 2368