This paper employs the extrinsic information transfer (EXIT) method, a technique imported from the analysis of the iterative decoding of error control codes, to study the performance of belief propagation in community detection in the presence of side information. We consider both the detection of a single (hidden) community, as well as the problem of identifying two symmetric communities. For single community detection, this paper demonstrates the suitability of EXIT to predict the asymptotic phase transition for weak recovery. More importantly, EXIT analysis is leveraged to produce useful insights such as the performance of belief propagation near the threshold. For two symmetric communities, the asymptotic residual error for belief propagation is calculated under finite-alphabet side information, generalizing a previous result with noisy labels. EXIT analysis is used to illuminate the effect of side information on community detection, its relative importance depending on the correlation of the graphical information with node labels, as well as the effect of side information on residual errors.
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 attention in many different fields, including computer science, statistics, social sciences, among others. Numerous approaches for community detection have been proposed in literature, from ad-hoc algorithms to systematic model-based approaches. The large number of available methods leads to a fundamental question: whether a certain method can provide consistent e…
Discovering community structure in complex networks is a mature field since a tremendous number of community detection methods have been introduced in the literature. Nevertheless, it is still very challenging for practioners to determine which method would be suitable to get insights into the structural information of the networks they study. Many recent efforts have been devoted to investigating various quality scores of the community structure, but the problem of distinguishing between different types of communities is still open. In this paper, we propose a comparative, extensive and empir…
Linkoping University（林雪平大学）；Umeå University（于默奥大学）；Swedish Defence Research Agency（瑞典国防研究局）
Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and clustering. In this paper, we present an ensemble method to improve community detection by aggregating the information found in an ensemble of community structures. This ensemble can found by re-sampling methods, multiple runs of a stochastic community detection method, or by several different community detection algorithms applied to the same network. The proposed me…
We study the community detection problem on a Gaussian mixture model, in which vertices are divided into $k\geq 2$ distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the threshold for the exact recovery of the maximum likelihood estimation. Applications include the community detection on hypergraphs.
Community detection is a fundamental problem in the analysis of complex networks. It is the analogue of clustering in network data mining. Within community detection methods, hierarchical algorithms are popular. However, their iterative nature and the need to recompute the structural properties used to split the network (i.e. edge betweenness in Girvan and Newman's algorithm), make them unsuitable for large network data sets. In this paper, we study how local structural network properties can be used as proxies to improve the efficiency of hierarchical community detection while, at the same ti…
Community detection is a fundamental problem in machine learning. While deep learning has shown great promise in many graphrelated tasks, developing neural models for community detection has received surprisingly little attention. The few existing approaches focus on detecting disjoint communities, even though communities in real graphs are well known to be overlapping. We address this shortcoming and propose a graph neural network (GNN) based model for overlapping community detection. Despite its simplicity, our model outperforms the existing baselines by a large margin in the task of communi…
University of California, Davis（加州大学戴维斯分校）；University of Exeter（埃克塞特大学）
A Health Service Area (HSA) is a group of geographic regions served by similar health care facilities. The delineation of HSAs plays a pivotal role in the characterization of health care services available in an area, enabling a better planning and regulation of health care services. Though Dartmouth HSAs have been the standard delineation for decades, previous work has recently shown an improved HSA delineation using a network-based approach, in which HSAs are the communities extracted by the Louvain algorithm in hospital-patient discharge networks. Given the existent heterogeneity of communi…
Bell Laboratories, Nokia（诺基亚贝尔实验室）；Princeton University（普林斯顿大学）
We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our method is inspired by detection in the benchmark Stochastic Block Model (SBM), where we provide sample complexity analysis and empirical study with SBM and real network data for binary as well as for the multi-class settings. The analysis also covers the most challenging case of sparse de…
Local network community detection aims to find a single community in a large network, while inspecting only a small part of that network around a given seed node. This is much cheaper than finding all communities in a network. Most methods for local community detection are formulated as ad-hoc optimization problems. In this work, we instead start from a generative model for networks with community structure. By assuming that the network is uniform, we can approximate the structure of unobserved parts of the network to obtain a method for local community detection. We apply this local approxima…
The Chinese University of Hong Kong（香港中文大学）；Georgia Institute of Technology（佐治亚理工学院）；Tencent AI Lab（腾讯人工智能实验室）
It has been demonstrated that adversarial graphs, i.e., graphs with imperceptible perturbations added, can cause deep graph models to fail on node/graph classification tasks. In this paper, we extend adversarial graphs to the problem of community detection which is much more difficult. We focus on black-box attack and aim to hide targeted individuals from the detection of deep graph community detection models, which has many applications in real-world scenarios, for example, protecting personal privacy in social networks and understanding camouflage patterns in transaction networks. We propose…
Community detection plays a key role in understanding graph structure. However, several recent studies showed that community detection is vulnerable to adversarial structural perturbation. In particular, via adding or removing a small number of carefully selected edges in a graph, an attacker can manipulate the detected communities. However, to the best of our knowledge, there are no studies on certifying robustness of community detection against such adversarial structural perturbation. In this work, we aim to bridge this gap. Specifically, we develop the first certified robustness guarantee …
Universidade Federal de São Paulo (UNIFESP)（圣保罗联邦大学）；Instituto Tecnológico de Aeronáutica (ITA)（航空技术研究所）
Several applications have a community structure where the nodes of the same community share similar attributes. Anomaly or outlier detection in networks is a relevant and widely studied research topic with applications in various domains. Despite a significant amount of anomaly detection frameworks, there is a dearth on the literature of methods that consider both attributed graphs and the community structure of the networks. This paper proposes a community-based anomaly detection algorithm using a spectral graph-based filter that includes the network community structure into the Laplacian mat…
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes, and average within and between community connectivities in an…
Community detection is a task of fundamental importance in social network analysis that can be used in a variety of knowledge-based domains. While there exist many works on community detection based on connectivity structures, they suffer from either considering the overlapping or non-overlapping communities. In this work, we propose a novel approach for general community detection through an integrated framework to extract the overlapping and non-overlapping community structures without assuming prior structural connectivity on networks. Our general framework is based on a primary node based …
The richness of definitions and features of the community-detection problem has led to an impressive body of literature. In fact, many community-detection methods and surveys have been introduced in recent years. The goal here is to present a state-of-the-art of the most mature research in this area. We will therefore concentrate on non-overlapping community detection with the basic graph model. In this chapter we will give an overview of the most influential approaches to community detection that encompass most of the main methods and techniques. A special focus will also be given to communit…
It is well-known that community detection methods based on modularity optimization often fails to discover small communities. Several objective functions used for community detection therefore involve a resolution parameter that allows the detection of communities at different scales. We provide an explicit upper bound on the community size of communities resulting from the optimization of several of these functions. We also show with a simple example that the use of the resolution parameter may artificially force the complete disaggregation of large and densely connected communities.
We introduce a novel algorithm of community detection that maintains dynamically a community structure of a large network that evolves with time. The algorithm maximizes the modularity index thanks to the construction of a randomized hierarchical clustering based on a Monte Carlo Markov Chain (MCMC) method. Interestingly, it could be seen as a dynamization of Louvain algorithm (see Blondel et Al, 2008) where the aggregation step is replaced by the hierarchical instrumental probability.
University of Washington（华盛顿大学）；University of California, San Diego（加州大学圣地亚哥分校）
We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of two blocks: above the threshold, there is a spectral algorithm which asymptotically almost surely constructs a partition of the hypergraph correlated with the true partition. Our method is a generalization to random hypergraphs of the method developed by Massoulié (2014) for spa…
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 information assigned to each vertex associated with the community to which it belongs. The problem addressed this paper is the detection of the community structure from the information of both the network structure and the vertex attribute data. Our approach is based on the Bayesian approach that models the posterior probability distribution of the community label…
Multiplex networks, a special type of multilayer networks, are increasingly applied in many domains ranging from social media analytics to biology. A common task in these applications concerns the detection of community structures. Many existing algorithms for community detection in multiplexes attempt to detect communities which are shared by all layers. In this article we propose a community detection algorithm, LART (Locally Adaptive Random Transitions), for the detection of communities that are shared by either some or all the layers in the multiplex. The algorithm is based on a random wal…
The problem of secure friend discovery on a social network has long been proposed and studied. The requirement is that a pair of nodes can make befriending decisions with minimum information exposed to the other party. In this paper, we propose to use community detection to tackle the problem of secure friend discovery. We formulate the first privacy-preserving and decentralized community detection problem as a multi-objective optimization. We design the first protocol to solve this problem, which transforms community detection to a series of Private Set Intersection (PSI) instances using Trun…
Community is a universal structure in various complex networks, and community detection is a fundamental task for network analysis. With the rapid growth of network scale, networks are massive, changing rapidly and could naturally be modeled as graph streams. Due to the limited memory and access constraint in graph streams, existing non-streaming community detection methods are no longer applicable. This raises an emerging need for online approaches. In this work, we consider the problem of uncovering the local community containing a few query nodes in graph streams, termed streaming local com…
Many methods have been proposed for community detection in networks, but most of them do not take into account additional information on the nodes that is often available in practice. In this paper, we propose a new joint community detection criterion that uses both the network edge information and the node features to detect community structures. One advantage our method has over existing joint detection approaches is the flexibility of learning the impact of different features which may differ across communities. Another advantage is the flexibility of choosing the amount of influence the fe…
Community describes the functional mechanism of a network, making community detection serve as a fundamental graph tool for various real applications like discovery of social circle. To date, a Symmetric and Non-negative Matrix Factorization (SNMF) model has been frequently adopted to address this issue owing to its high interpretability and scalability. However, most existing SNMF-based community detection methods neglect the high-order connection patterns in a network. Motivated by this discovery, in this paper, we propose a High-Order Proximity (HOP)-incorporated, Symmetry and Graph-regular…
Community detection is an important research topic in graph analytics that has a wide range of applications. A variety of static community detection algorithms and quality metrics were developed in the past few years. However, most real-world graphs are not static and often change over time. In the case of streaming data, communities in the associated graph need to be updated either continuously or whenever new data streams are added to the graph, which poses a much greater challenge in devising good community detection algorithms for maintaining dynamic graphs over streaming data. In this pap…
We introduce a new paradigm that is important for community detection in the realm of network analysis. Networks contain a set of strong, dominant communities, which interfere with the detection of weak, natural community structure. When most of the members of the weak communities also belong to stronger communities, they are extremely hard to be uncovered. We call the weak communities the hidden community structure. We present a novel approach called HICODE (HIdden COmmunity DEtection) that identifies the hidden community structure as well as the dominant community structure. By weakening the…
University of Calabria（卡拉布里亚大学）；Institute for High Performance Computing and Networking, ICAR-CNR（高性能计算与网络研究所，ICAR-CNR）
The community deception problem is about how to hide a target community C from community detection algorithms. The need for deception emerges whenever a group of entities (e.g., activists, police enforcements) want to cooperate while concealing their existence as a community. In this paper we introduce and formalize the community deception problem. To solve this problem, we describe algorithms that carefully rewire the connections of C's members. We experimentally show how several existing community detection algorithms can be deceived, and quantify the level of deception by introducing a dece…
Community detection aims to reveal the community structure in a social network, which is one of the fundamental problems. In this paper we investigate the community detection problem based on the concept of terminal set. A terminal set is a group of users within which any two users belong to different communities. Although the community detection is hard in general, the terminal set can be very helpful in designing effective community detection algorithms. We first present a 2-approximation algorithm running in polynomial time for the original community detection problem. In the other issue, i…
Community detection in social networks is widely studied because of its importance in uncovering how people connect and interact. However, little attention has been given to community structure in Facebook public pages. In this study, we investigate the community detection problem in Facebook newsgroup pages. In particular, to deal with the diversity of user activities, we apply multi-view clustering to integrate different views, for example, likes on posts and likes on comments. In this study, we explore the community structure in not only a given single page but across multiple pages. The re…
Community detection has been well studied recent years, but the more realistic case of mixed membership community detection remains a challenge. Here, we develop an efficient spectral algorithm Mixed-ISC based on applying more than K eigenvectors for clustering given K communities for estimating the community memberships under the degree-corrected mixed membership (DCMM) model. We show that the algorithm is asymptotically consistent. Numerical experiments on both simulated networks and many empirical networks demonstrate that Mixed-ISC performs well compared to a number of benchmark methods fo…
Shared travel has gradually become one of the hot topics discussed on social networking platforms such as Micro Blog. In a timely manner, deeper network community detection on the evaluation content of shared travel in social networks can effectively conduct research and analysis on the public opinion orientation related to shared travel, which has great application prospects. The existing community detection algorithms generally measure the similarity of nodes in the network from the perspective of spatial distance. This paper proposes a Community detection algorithm based on Textual content …
Community detection refers to the task of discovering groups of vertices sharing similar properties or functions so as to understand the network data. With the recent development of deep learning, graph representation learning techniques are also utilized for community detection. However, the communities can only be inferred by applying clustering algorithms based on learned vertex embeddings. These general cluster algorithms like K-means and Gaussian Mixture Model cannot output much overlapped communities, which have been proved to be very common in many real-world networks. In this paper, we…
Community detection is a fundamental task in social network analysis. In this paper, first we develop an endorsement filtered user connectivity network by utilizing Heider's structural balance theory and certain Twitter triad patterns. Next, we develop three Nonnegative Matrix Factorization frameworks to investigate the contributions of different types of user connectivity and content information in community detection. We show that user content and endorsement filtered connectivity information are complementary to each other in clustering politically motivated users into pure political commun…
Community detection plays an important role in understanding and exploiting the structure of complex systems. Many algorithms have been developed for community detection using modularity maximization or other techniques. In this paper, we formulate the community detection problem as a constrained nonsmooth optimization problem on the compact Stiefel manifold. A Riemannian projected proximal gradient method is proposed and used to solve the problem. To the best of our knowledge, this is the first attempt to use Riemannian optimization for community detection problem. Numerical experimental resu…
This report presents a very simple algorithm for overlaping community-detection in large graphs under constraints such as the minimum and maximum number of members allowed. The algorithm is based on the simulation of random walks and measures the entropy of each random walk to detect the discovery of a community.
Tianjin University（天津大学）；Monash University（莫纳什大学）；Macquarie University（麦考瑞大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Washington University（华盛顿大学）
Community detection, a fundamental task for network analysis, aims to partition a network into multiple sub-structures to help reveal their latent functions. Community detection has been extensively studied in and broadly applied to many real-world network problems. Classical approaches to community detection typically utilize probabilistic graphical models and adopt a variety of prior knowledge to infer community structures. As the problems that network methods try to solve and the network data to be analyzed become increasingly more sophisticated, new approaches have also been proposed and d…
The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches community detection in graphs by constructing Markov random walks on the graphs. The mixing properties of the random walk are then used to identify communities. We use coupling from the past as an algorithmic primitive to translate the mixing properties of the walk into revealing the community structure of the graph. We analyze the performance of our algorithms on…
Community detection plays an important role in social networks, since it can help to naturally divide the network into smaller parts so as to simplify network analysis. However, on the other hand, it arises the concern that individual information may be over-mined, and the concept community deception thus is proposed to protect individual privacy on social networks. Here, we introduce and formalize the problem of community detection attack and develop efficient strategies to attack community detection algorithms by rewiring a small number of connections, leading to individual privacy protectio…
Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called "ground truth" communities. This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on those known communities. However, there are …
The problem of finding the spatial-aware community for a given node has been defined and investigated in geo-social networks. However, existing studies suffer from two limitations: a) the criteria of defining communities are determined by parameters, which are difficult to set; b) algorithms may require global information and are not suitable for situations where the network is incomplete. Therefore, we propose spatial-aware local community detection (SLCD), which finds the spatial-aware local community with only local information and defines the community based on the difference in the sparse…
In this paper, we consider the community detection problem in signed networks, where there are two types of edges: positive edges (friends) and negative edges (enemies). One renowned theorem of signed networks, known as Harary's theorem, states that structurally balanced signed networks are clusterable. By viewing each cycle in a signed network as a parity-check constraint, we show that the community detection problem in a signed network with two communities is equivalent to the decoding problem for a parity-check code. We also show how one can use two renowned decoding algorithms in error- co…
Much of the community detection literature studies structural communities, communities defined solely by the connectivity patterns of the network. Often, networks contain additional metadata which can inform community detection such as the grade and gender of students in a high school social network. In this work, we introduce a tuning parameter to the content map equation that allows users of the Infomap community detection algorithm to control the metadata's relative importance for identifying network structure. On synthetic networks, we show that our algorithm can overcome the structural de…
Understanding community structure in social media is critical due to its broad applications such as friend recommendations, link predictions and collaborative filtering. However, there is no widely accepted definition of community in literature. Existing work use structure related metrics such as modularity and function related metrics such as ground truth to measure the performance of community detection algorithms, while ignoring an important metric, size of the community. [1] suggests that the size of community with strong ties in social media should be limited to 150. As we discovered in t…
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general network model where two arbitrarily connected communities are interconnected by random external edges. Specifically, the community detection performance transitions from almost perfect detectability to low detectability as the inter-community edge connection probability exceeds …
The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more realistic networks where edges are heterogeneously distributed within and between communities. Using the random graph properties, we establish asymptotic theoretical bounds on the resolution parameter for which the generalized modularity maximization performs well. From this new perspective on random graph model, we find the resolution limit of modularity maximi…
Many evolving complex systems can be modeled via dynamic networks. An important problem in dynamic network research is community detection, which identifies groups of topologically related nodes. Typically, this problem is approached by assuming either that each time point has a distinct community organization or that all time points share one community organization. In reality, the truth likely lies between these two extremes, since some time periods can have community organization that evolves while others can have community organization that stays the same. To find the compromise, we consid…
While there has been a plethora of approaches for detecting disjoint communities from real-world complex networks, some methods for detecting overlapping community structures have also been recently proposed. In this work, we argue that, instead of developing separate approaches for detecting overlapping communities, a promising alternative is to infer the overlapping communities from multiple disjoint community structures. We propose an ensemble-based approach, called EnCoD, that leverages the solutions produced by various disjoint community detection algorithms to discover the overlapping co…
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 in a complete graph in which the graph edges are drawn from either a set of Gaussian distributions with community-dependent means and variances, or a set of exponential distributions with community-dependent means. For each case, we introduce a new semi-metric that describes sufficient and necessary conditions of exact recovery. The necessary and sufficient…
This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees. This survey is not int…
