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We study the community detection problem on a Gaussian mixture model, in which vertices are divided into $kgeq 2$ distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the threshold for the exact recovery of the maximum likelihood estimation. Applications include the community detection on hypergraphs.
We study the vertex classification problem on a graph whose vertices are in $k (kgeq 2)$ different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal. The ob
Community detection is a key task to further understand the function and the structure of complex networks. Therefore, a strategy used to assess this task must be able to avoid biased and incorrect results that might invalidate further analyses or ap
In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the $m-$ShSBM, we
We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an end-to-end commun
Analyzing the groups in the network based on same attributes, functions or connections between nodes is a way to understand network information. The task of discovering a series of node groups is called community detection. Generally, two types of in