Beyond Rank-1: Discovering Rich Community Structure in Multi-Aspect Graphs

How are communities in real multi-aspect or multi-view graphs structured? How we can effectively and concisely summarize and explore those communities in a high-dimensional, multi-aspect graph without losing important information? State-of-the-art studies focused on patterns in single graphs, identifying structures in a single snapshot of a large network or in time evolving graphs and stitch them over time. However, to the best of our knowledge, there is no method that discovers and summarizes community structure from a multi-aspect graph, by jointly leveraging information from all aspects. State-of-the-art in multi-aspect/tensor community extraction is limited to discovering clique structure in the extracted communities, or even worse, imposing clique structure where it does not exist. In this paper we bridge that gap by empowering tensor-based methods to extract rich community structure from multi-aspect graphs. In particular, we introduce cLL1, a novel constrained Block Term Tensor Decomposition, that is generally capable of extracting higher than rank-1 but still interpretable structure from a multi-aspect dataset. Subsequently, we propose RichCom, a community structure extraction and summarization algorithm that leverages cLL1to identify rich community structure (e.g., cliques, stars, chains, etc) while leveraging higher-order correlations between the different aspects of the graph. Our contributions are four-fold: (a) Novel algorithm: we develop cLL1, an efficient framework to extract rich and interpretable structure from general multi-aspect data; (b) Graph summarization and exploration: we provide RichCom, a summarization and encoding scheme to discover and explore structures of communities identified by cLL1; (c) Multi-aspect graph generator: we provide a simple and effective synthetic multi-aspect graph generator, and (d) Real-world utility: we present empirical results on small and large real datasets that demonstrate performance on par or superior to existing state-of-the-art.