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Fast and Guaranteed Learning of Overlapping Communities via Tensor Methods
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A community refers to a group of related nodes in a network. For instance, in a social network, it can represent individuals with shared interests or beliefs, and in a gene network, it can represent genes with common regulatory mechanisms, and so on. Detecting hidden communities in observed networks is an important problem. However, most previous approaches assume non-overlapping communities where a node can belong to at most one community. In contrast, we provide a guaranteed approach for detecting overlapping communities, when the network is generated from a class of probabilistic mixed membership block models. Our approach is based on fast and scalable tensor decompositions and linear algebraic operations. We provide guaranteed recovery of community memberships and establish a finite sample analysis of our algorithm. Our theoretical results match the best known scaling requirements in the special case of the popular stochastic block model (which has non-overlapping communities).
We have deployed the algorithm on GPUs, and our code design involves a careful optimization of GPU -CPU storage and communication. Our method is extremely fast and accurate. For instance, on a real dataset consisting of yelp reviews, with about 40,000 nodes, and about 500 hidden communities, our method takes under 30 minutes to run to convergence, and recovers communities with extremely high accuracy (with error of about 6%). Thus, our approach is fast, scalable and accurate for detecting overlapping communities.
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