Abstract
Recent research in the domain of computed graph embeddings has shown that graph homomorphism numbers constitute expressive features that are well-suited for machine learning tasks such as graph classification. In this work-in-progress paper, we attempt to make this methodology scalable by obtaining additive approximations to graph homomorphism densities via a simple sampling algorithm. We show in experiments that these approximate homomorphism densities perform as well as homomorphism numbers on standard graph classification datasets. Moreover, we show that, unlike algorithms that compute homomorphism numbers, our sampling algorithm is highly scalable to larger graphs.
Supported by Agence Nationale de la Recherche (ANR), projects STAP (ANR-17-CE23-0021) and ESIGMA (ANR-17-CE23-0010). F. Yger acknowledges the support of the ANR as part of the “Investissements d’avenir” program (ANR-19-P3IA-0001, PRAIRIE 3IA Institute).
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Notes
- 1.
Standard datasets contain relatively sparse graphs which means that the corresponding complement graphs are dense. Dense graphs have larger homomorphism densities which are easier to detect at fixed precision and more amenable for training machine learning models.
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Beaujean, P., Sikora, F., Yger, F. (2021). Graph Homomorphism Features: Why Not Sample?. In: Kamp, M., et al. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2021. Communications in Computer and Information Science, vol 1524. Springer, Cham. https://doi.org/10.1007/978-3-030-93736-2_17
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