Related papers: Performance of a community detection algorithm bas…
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle…
We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant…
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…
We study the problem of community detection in a random hypergraph model which we call the stochastic block model for $k$-uniform hypergraphs ($k$-SBM). We investigate the exact recovery problem in $k$-SBM and show that a sharp phase…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
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…
This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community…
We consider the problem of estimating the number of communities in a weighted balanced Stochastic Block Model. We construct hypothesis tests based on semidefinite programming and with a statistic coming from a GOE matrix to distinguish…
We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We…
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…
Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts,…
Many statistical inference problems correspond to recovering the values of a set of hidden variables from sparse observations on them. For instance, in a planted constraint satisfaction problem such as planted 3-SAT, the clauses are sparse…
Motivated by social network analysis and network-based recommendation systems, we study a semi-supervised community detection problem in which the objective is to estimate the community label of a new node using the network topology and…
Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper,…
Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…
We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…
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),…
Community detection or clustering is a fundamental task in the analysis of network data. Many real networks have a bipartite structure which makes community detection challenging. In this paper, we consider a model which allows for matched…