Related papers: Exact Label Recovery in Euclidean Random Graphs
This paper considers the problem of label recovery in random graphs and matrices. Motivated by transitive behavior in real-world networks (i.e., ``the friend of my friend is my friend''), a recent line of work considers spatially-embedded…
We study the problem of exact community recovery in the Geometric Stochastic Block Model (GSBM), where each vertex has an unknown community label as well as a known position, generated according to a Poisson point process in $\mathbb{R}^d$.…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which…
We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex…
Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its…
We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic…
Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the…
We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…
This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph stochastic block model (d-HSBM), wherein n nodes are partitioned into k disjoint communities with relative sizes (p1,..., pk). Each subset of…
Network clustering tackles the problem of identifying sets of nodes (communities) that have similar connection patterns. However, in many scenarios, nodes also have attributes that are correlated with the clustering structure. Thus, network…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models…
Motivated by applications such as discovering strong ties in social networks and assembling genome subsequences in biology, we study the problem of recovering a hidden $2k$-nearest neighbor (NN) graph in an $n$-vertex complete graph, whose…
In community detection, the exact recovery of communities (clusters) has been mainly investigated under the general stochastic block model with edges drawn from Bernoulli distributions. This paper considers the exact recovery of communities…
We study the vertex classification problem on a graph whose vertices are in $k\ (k\geq 2)$ different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily…
We consider the problem of exact community recovery in the Labeled Stochastic Block Model (LSBM) with $k$ communities, where each pair of vertices is associated with a label from the set $\{0,1, \dots, L\}$. A pair of vertices from…
We analyze directed, unweighted graphs obtained from $x_i\in \mathbb{R}^d$ by connecting vertex $i$ to $j$ iff $|x_i - x_j| < \epsilon(x_i)$. Examples of such graphs include $k$-nearest neighbor graphs, where $\epsilon(x_i)$ varies from…
Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first…