Related papers: Model Selection for Degree-corrected Block Models
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…
Network data are observed in various applications where the individual entities of the system interact with or are connected to each other, and often these interactions are defined by their associated strength or importance. Clustering is a…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
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…
In network analysis, developing a unified theoretical framework that can compare methods under different models is an interesting problem. This paper proposes a partial solution to this problem. We summarize the idea of using separation…
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…
Characterizing large-scale organization in networks, including multilayer networks, is one of the most prominent topics in network science and is important for many applications. One type of mesoscale feature is community structure, in…
For the degree corrected stochastic block model in the presence of arbitrary or even adversarial outliers, we develop a convex-optimization-based clustering algorithm that includes a penalization term depending on the positive deviation of…
The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing…
We propose a new dynamic stochastic blockmodel that focuses on the analysis of interaction lengths in networks. The model does not rely on a discretization of the time dimension and may be used to analyze networks that evolve continuously…
An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial…
The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with…
In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also…
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 generalizes the random geometric…