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Much of the complexity of social, biological, and engineered systems arises from a network of complex interactions connecting many basic components. Network analysis tools have been successful at uncovering latent structure termed communities in such networks. However, some of the most interesting structure can be difficult to uncover because it is obscured by the more dominant structure. Our previous work proposes a general structure amplification technique called HICODE that uncovers many layers of functional hidden structure in complex networks. HICODE incrementally weakens dominant structure through randomization allowing the hidden functionality to emerge, and uncovers these hidden structure in real-world networks that previous methods rarely uncover. In this work, we conduct a comprehensive and systematic theoretical analysis on the hidden community structure. In what follows, we define multi-layer stochastic block model, and provide theoretical support using the model on why the existence of hidden structure will make the detection of dominant structure harder compared with equivalent random noise. We then provide theoretical proofs that the iterative reducing methods could help promote the uncovering of hidden structure as well as boosting the detection quality of dominant structure.
We provide the first information theoretic tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same latent communities. Our work bridges recent theoretical b
We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently aggregate signa
Hidden community is a new graph-theoretical concept recently proposed [4], in which the authors also propose a meta-approach called HICODE (Hidden Community Detection) for detecting hidden communities. HICODE is demonstrated through experiments that
With ever-increasing amounts of online information available, modeling and predicting individual preferences-for books or articles, for example-is becoming more and more important. Good predictions enable us to improve advice to users, and obtain a b
Methods for ranking the importance of nodes in a network have a rich history in machine learning and across domains that analyze structured data. Recent work has evaluated these methods though the seed set expansion problem: given a subset $S$ of nod