Link prediction with hyperbolic geometry

Maksim Kitsak,Ivan Voitalov,Dmitri Krioukov

doi:10.1103/physrevresearch.2.043113

Maksim Kitsak, Ivan Voitalov + Show 1 more

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https://doi.org/10.1103/physrevresearch.2.043113

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Abstract

Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with hyperbolic latent spaces has a number of attractive properties suggesting it must be a powerful tool to predict links, but the past work in this direction reported mixed results. Here we perform systematic investigation of the utility of latent hyperbolic geometry for link prediction in networks. We first show that some measures of link prediction accuracy are extremely sensitive with respect to inaccuracies in the inference of latent hyperbolic coordinates of nodes, so that we develop a new coordinate inference method that maximizes the accuracy of such inference. Applying this method to synthetic and real networks, we then find that while there exists a multitude of competitive methods to predict obvious easy-to-predict links, among which hyperbolic link prediction is rarely the best but often competitive, it is the best, often by far, when the task is to predict less obvious missing links that are really hard to predict. These links include missing links in incomplete networks with large fractions of missing links, missing links between nodes that do not have any common neighbors, and missing links between dissimilar nodes at large latent distances. Overall these results suggest that the harder a specific link prediction task is, the more seriously one should consider using hyperbolic geometry.

Highlights

IntroductionLatent space network models [17–21] offer an intuitive and simple approach to link prediction
Link prediction is a paradigmatic example of forecasting network dynamics [1–4], with diverse applications including the reconstruction of networks based on partial data [5–7] and prediction of future social ties [1,8,9], protein interactions [10–12], and user ratings in recommender systems [13–16]
We evaluate the accuracy of the HYPERLINK as well as other link prediction methods through random link removal experiments

Summary

Introduction

Latent space network models [17–21] offer an intuitive and simple approach to link prediction. In these models, network nodes are points in a latent space, while connections are established with probabilities that decrease with latent distances between nodes. Latent distances model similarity between nodes, and the main idea behind these models is to model homophily: more similar nodes are more likely to be linked. Link prediction reduces to ranking unconnected node pairs in the order of increasing latent distances between them: the closer the two unlinked nodes in the latent space, the higher the probability of a missing link [4,22–24]

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