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

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.

We introduce PieClam, a novel model for analyzing graphs, like social networks. Our method interprets any graph as a collection of communities. PieClam identifies two types of communities within networks: inclusive communities, where nodes are closely connected, and exclusive communities, where nodes are strongly disconnected. As opposed to past methods, which only considered inclusive communities, our dual approach helps in better understanding the structure and behavior of networks. Moreover, unlike traditional methods, PieClam not only looks at how nodes in a graph are connected but also learns a way to randomly generate graphs which are similar to the given graph. On the theoretical side, we developed a new way to measure similarity between networks, called the log cut distance, which allows us to prove that PieClam is guaranteed to accurately represent and analyze any network whatsoever. On the application side, our experiments show that PieClam performs well in detecting anomalies in networks and predicting unseen connections in graphs.