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Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…
Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs…
We study the problem of exact community recovery in general, two-community block models, in the presence of node-attributed $side$ $information$. We allow for a very general side information channel for node attributes, and for pairwise…
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…
In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM),…
The present work is concerned with community detection. Specifically, we consider a random graph drawn according to the stochastic block model~: its vertex set is partitioned into blocks, or communities, and edges are placed randomly and…
Denote by $A$ the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing $\langle A-E\{A\},X\rangle$ over the set of positive semidefinite matrices $X$ with diagonal entries $X_{ii}=1$.…
Community detection approaches resolve complex networks into smaller groups (communities) that are expected to be relatively edge-dense and well-connected. The stochastic block model (SBM) is one of several approaches used to uncover…
In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erd\H{o}s-R\'enyi (ER) graph embedded in a larger and sparser ER graph, in the presence of…
The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users (represented by adjacency matrix of a graph). There has been significant…
In statistical network analysis, we often assume either the full network is available or multiple subgraphs can be sampled to estimate various global properties of the network. However, in a real social network, people frequently make…
Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
We propose a new algorithm to detect the community structure in a network that utilizes both the network structure and vertex attribute data. Suppose we have the network structure together with the vertex attribute data, that is, the…
Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic…
We consider the problem of recovering a binary rating matrix as well as clusters of users and items based on a partially observed matrix together with side-information in the form of social and item similarity graphs. These two graphs are…
Community detection is a fundamental problem in computational sciences with extensive applications in various fields. The most commonly used methods are the algorithms designed to maximize modularity over different partitions of the network…