PieClam: A Universal Graph Autoencoder Based on Overlapping Inclusive and Exclusive Communities

摘要

We propose PieClam (Prior Inclusive Exclusive Cluster Affiliation Model): a graph autoencoder, where nodes are embedded into a code space by an algorithm that maximizes the log-likelihood of the decoded graph. PieClam is a community affiliation model that extends well-known methods like BigClam in two main manners. First, instead of the decoder being defined via pairwise interactions between the nodes in the code space, we also incorporate a learned prior on the distribution of nodes in the code space, turning our method into a graph generative model. Secondly, we generalize the notion of communities by allowing not only sets of nodes with strong connectivity, which we call inclusive communities, but also sets of nodes with strong disconnection, which we call exclusive communities. By introducing a new graph similarity measure, called the log cut distance, we show that PieClam is a universal autoencoder, able to uniformly approximately reconstruct any graph. Our method is shown to obtain competitive performance in graph anomaly detection and link prediction benchmarks.