
Submatrix localization via message passing
The principal submatrix localization problem deals with recovering a K× ...
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Finding One Community in a Sparse Graph
We consider a random sparse graph with bounded average degree, in which ...
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Recovering a Hidden Community in a Preferential Attachment Graph
A message passing algorithm (MP) is derived for recovering a dense subgr...
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A Fast Hadamard Transform for Signals with Sublinear Sparsity in the Transform Domain
A new iterative low complexity algorithm has been presented for computin...
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Density Evolution in the Degreecorrelated Stochastic Block Model
There is a recent surge of interest in identifying the sharp recovery th...
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Robustness of Community Detection to Random Geometric Perturbations
We consider the stochastic block model where connection between vertices...
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NearPerfect Recovery in the OneDimensional Latent Space Model
Suppose a graph G is stochastically created by uniformly sampling vertic...
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Recovering a Hidden Community Beyond the Spectral Limit in O(E ^*V) Time
Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on recovery of the community based on the graph G, with o(K) misclassified vertices on average, in the sublinear regime n^1o(1)≤ K ≤ o(n). It is shown that such recovery is attainable by a belief propagation algorithm running for ^∗ n+O(1) iterations, if λ =K^2(pq)^2/((nK)q), the signaltonoise ratio, exceeds 1/e, with the total time complexity O(E ^*n). Conversely, if λ≤ 1/e, no local algorithm can asymptotically outperform trivial random guessing. By analyzing a linear messagepassing algorithm that corresponds to applying power iteration to the nonbacktracking matrix of the graph, we provide evidence to suggest that spectral methods fail to recovery the community if λ≤ 1. In addition, the belief propagation algorithm can be combined with a lineartime voting procedure to achieve the information limit of exact recovery (correctly classify all vertices with high probability) for all K >n/ n( ρ_ BP +o(1) ), where ρ_ BP is a function of p/q.
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