Hidden community is a new graph-theoretical concept recently proposed [4], in which the authors also propose a meta-approach called HICODE (Hidden Community Detection) for detecting hidden communities. HICODE is demonstrated through experiments that it is able to uncover previously overshadowed weak layers and uncover both weak and strong layers at a higher accuracy. However, the authors provide no theoretical guarantee for the performance. In this work, we focus on the theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent of each other and each layer is generated by stochastic block model. We bridge their gap through two-layer stochastic block model networks in the following aspects: 1) we show that partitions that locally optimize modularity correspond to grounded layers, indicating modularity-optimizing algorithms can detect strong layers; 2) we prove that when reducing found layers, HICODE increases absolute modularities of all unreduced layers, showing its layer reduction step makes weak layers more detectable. Our work builds a solid theoretical base for HICODE, demonstrating that it is promising in uncovering both weak and strong layers of communities in two-layer networks.
We introduce a new conception of community structure, which we refer to as hidden community structure. Hidden community structure refers to a specific type of overlapping community structure, in which the detection of weak, but meaningful, communities is hindered by the presence of stronger communities. We present Hidden Community Detection HICODE, an algorithm template that identifies both the strong, dominant community structure as well as the weaker, hidden community structure in networks. HICODE begins by first applying an existing community detection algorithm to a network, and then remov…
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…
Currently, we are overwhelmed by a deluge of experimental data, and network physics has the potential to become an invaluable method to increase our understanding of large interacting datasets. However, this potential is often unrealized for two reasons: uncovering the hidden community structure of a network, known as community detection, is difficult, and further, even if one has an idea of this community structure, it is not a priori obvious how to efficiently use this information. Here, to address both of these issues, we, first, identify optimal community structure of given networks in ter…
Huazhong University of Science and Technology（华中科技大学）；Cornell University（康奈尔大学）
Hidden community is a useful concept proposed recently for social network analysis. To handle the rapid growth of network scale, in this work, we explore the detection of hidden communities from the local perspective, and propose a new method that detects and boosts each layer iteratively on a subgraph sampled from the original network. We first expand the seed set from a single seed node based on our modified local spectral method and detect an initial dominant local community. Then we temporarily remove the members of this community as well as their connections to other nodes, and detect all…
Certain crimes are hardly committed by individuals but carefully organised by group of associates and affiliates loosely connected to each other with a single or small group of individuals coordinating the overall actions. A common starting point in understanding the structural organisation of criminal groups is to identify the criminals and their associates. Situations arise in many criminal datasets where there is no direct connection among the criminals. In this paper, we investigate ties and community structure in crime data in order to understand the operations of both traditional and cyb…
Community structure in networks has been investigated from many viewpoints, usually with the same end result: a community detection algorithm of some kind. Recent research offers methods for combining the results of such algorithms into timelines of community evolution. This paper investigates community detection and tracking from the data fusion perspective. We avoid the kind of hard calls made by traditional community detection algorithms in favor of retaining as much uncertainty information as possible. This results in a method for directly estimating the probabilities that pairs of nodes a…
Communities are ubiquitous in nature and society. Individuals that share common properties often self-organize to form communities. Avoiding the shortages of computation complexity, pre-given information and unstable results in different run, in this paper, we propose a simple and effcient method to deepen our understanding of the emergence and diversity of communities in complex systems. By introducing the rational random selection, our method reveals the hidden deterministic and normal diverse community states of community structure. To demonstrate this method, we test it with real-world sys…
Advances in public transit modeling and smart card technologies can reveal detailed contact patterns of passengers. A natural way to represent such contact patterns is in the form of networks. In this paper we utilize known contact patterns from a public transit assignment model in a major metropolitan city, and propose the development of two novel network structures, each of which elucidate certain aspects of passenger travel behavior. We first propose the development of a transfer network, which can reveal passenger groups that travel together on a given day. Second, we propose the developme…
Critical analysis of the state of the art is a necessary task when identifying new research lines worthwhile to pursue. To such an end, all the available work related to the field of interest must be taken into account. The key point is how to organize, analyze, and make sense of the huge amount of scientific literature available today on any topic. To tackle this problem, we present here a bibliometric approach to Systematic Mapping Studies (SMS). Thus, a modify SMS protocol is used relying on the scientific references metadata to extract, process and interpret the wealth of information conta…
We study the structural properties of large scale collaboration in online communities of innovation and the role that position in the community plays in determining knowledge contribution. Contrary to previous research, we argue for a more local perspective when examining online collaboration. We demonstrate that a member's centrality and spanning within his/her local neighborhood is a better predictor of contribution than global centrality and spanning within the whole community. We contribute both theoretically and methodologically to research on large scale collaboration. On the theoretical…
We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according to their opinions or preferences on a topic. For learning these properties, we propose a nonparametric, unsupervised, and scalable graph scan procedure that is, in addition, robust against a class of powerful adversaries. In our setup, one of the communities can fall under the influence of a knowledgeable adversarial leader, who knows the full network structure, has unlimited comp…
In community detection, datasets often suffer a sampling bias for which nodes which would normally have a high affinity appear to have zero affinity. This happens for example when two affine users of a social network were not exposed to one another. Community detection on this kind of data suffers then from considering affine nodes as not affine. To solve this problem, we explicitly model the (non-)exposure mechanism in a Bayesian community detection framework, by introducing a set of additional hidden variables. Compared to approaches which do not model exposure, our method is able to better …
The analysis of multilayer networks is among the most active areas of network science, and there are now several methods to detect dense "communities" of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to differen…
A Local Perspective-based Model for Overlapping Community Detection
College of Computer Science & Technology, Qingdao University（青岛大学计算机科学与技术学院）；College of Engineering, China Agricultural University（中国农业大学工程学院）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）
We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij} \sim P$ if $i, j$ are both in the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$. We identify a sufficient condition and a necessary condition for the success of SDP for the general model. For both the Bernoulli case ($P={\rm Bern}(p)$ and $Q={\rm Bern}(q)$ with $p>q$) and the Gaussian case ($P=\mathcal{N}(μ,1)$…
Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem - community detection - in multilayer networks are still limited. In this work, we first introduce the multilayer network mode…
The study of networks has emerged in diverse disciplines as a means of analyzing complex relationship data. Beyond graph analysis tasks like graph query processing, link analysis, influence propagation, there has recently been some work in the area of outlier detection for information network data. Although various kinds of outliers have been studied for graph data, there is not much work on anomaly detection from edge-attributed graphs. In this paper, we introduce a method that detects novel outlier graph nodes by taking into account the node data and edge data simultaneously to detect anomal…
Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the graph G, with o(K) misclassified vertices on average, in the sublinear regime $n^{1-o(1)} \leq K \leq o(n).$ A critical parameter is the effective signal-to-noise ratio $λ=K^2(p-q)^2/((n-K)q)$, with $λ=1$ corresponding to the Kesten-Stigum threshold. We show that a belief propaga…
A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that contain the information collected from multiple perspectives have been generated. The conventional models designed for single perspective networks fail to depict the diverse topological properties of such systems, so multilayer network models aiming at describing the structure of these networks emerge. As a major concern in network science, decomposing the networ…
Community detection and link prediction are both of great significance in network analysis, which provide very valuable insights into topological structures of the network from different perspectives. In this paper, we propose a novel community detection algorithm with inclusion of link prediction, motivated by the question whether link prediction can be devoted to improving the accuracy of community partition. For link prediction, we propose two novel indices to compute the similarity between each pair of nodes, one of which aims to add missing links, and the other tries to remove spurious ed…
To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as degree centrality, betweenness centrality, or PageRank neglect the community structure found in real-world networks. To study node importance based on network flows from a mesoscopic perspective, we analytically derive a community-aware information-theoretic centrality score based on network flow and the coding principles behind the map equation: map equation c…
Online question-and-answer (Q&A) communities provide convenient and innovative ways for participants to share information and collaboratively solve problems with others. A growing challenge for those Q&A communities is to encourage and maintain ongoing user participation. From the perspective of motivational affordances, this study proposes a research framework to explain the effect of content commenting on user continuance behavior in online Q&A communities. The moderating role of participant's tenure in the relationship between content commenting and user continuance is also explored. Using …
In many applications, it is common practice to obtain a network from interaction counts by thresholding each pairwise count at a prescribed value. Our analysis calls attention to the dependence of certain methods, notably Newman--Girvan modularity, on the choice of threshold. Essentially, the threshold either separates the network into clusters automatically, making the algorithm's job trivial, or erases all structure in the data, rendering clustering impossible. By fitting the original interaction counts as given, we show that minor modifications to classical statistical methods outperform th…
University of Massachusetts（马萨诸塞大学）；Technicolor（特艺集团）；INRIA-ENS（法国国家信息与自动化研究所-巴黎高等师范学院）；INRIA-Microsoft Research Joint Centre（法国国家信息与自动化研究所-微软研究院联合中心）
We consider the problem of community detection from observed interactions between individuals, in the context where multiple types of interaction are possible. We use labelled stochastic block models to represent the observed data, where labels correspond to interaction types. Focusing on a two-community scenario, we conjecture a threshold for the problem of reconstructing the hidden communities in a way that is correlated with the true partition. To substantiate the conjecture, we prove that the given threshold correctly identifies a transition on the behaviour of belief propagation from inse…
In the last few years many real-world networks have been found to show a so-called community structure organization. Much effort has been devoted in the literature to develop methods and algorithms that can efficiently highlight this hidden structure of the network, traditionally by partitioning the graph. Since network representation can be very complex and can contain different variants in the traditional graph model, each algorithm in the literature focuses on some of these properties and establishes, explicitly or implicitly, its own definition of community. According to this definition it…
Instagram has been increasingly used as a source of information especially among the youth. As a result, political figures now leverage the platform to spread opinions and political agenda. We here analyze online discussions on Instagram, notably in political topics, from a network perspective. Specifically, we investigate the emergence of communities of co-commenters, that is, groups of users who often interact by commenting on the same posts and may be driving the ongoing online discussions. In particular, we are interested in salient co-interactions, i.e., interactions of co-commenters that…
Community detection in social networks is a problem with considerable interest, since, discovering communities reveals hidden information about networks. There exist many algorithms to detect inherent community structures and recently few of them are investigated on social networks. However, it is non-trivial to decide the best approach in the presence of diverse nature of graphs, in terms of density and sparsity, and inadequate analysis of the results. Therefore, in this study, we analyze and compare various algorithms to detect communities in two networks, namely social and road networks, wi…
Various attempts have been made in recent years to solve the Resolution Limit (RL) problem in community detection by considering variants of the modularity metric in the detection algorithms. These metrics purportedly largely mitigate the RL problem and are preferable to modularity in many realistic scenarios. However, they are not generally suitable for analyzing weighted networks or for detecting hierarchical community structure. Resolution limit problems can be complicated, though, and in particular it can be unclear when it should be considered as problem. In this paper, we introduce a met…
The Naming Games (NG) are agent-based models for agreement dynamics, peer pressure and herding in social networks, and protocol selection in autonomous ad-hoc sensor networks. By introducing a small noise term to the NG, the resulting Markov Chain model called Noisy Naming Games (NNG) are ergodic, in which all partial consensus states are recurrent. By using Gibbs-Markov equivalence we show how to get the NNG's stationary distribution in terms of the local specification of a related Markov Random Field (MRF). By ordering the partially-synchronized states according to their Gibbs energy, taken …
National Institute of Technology, Silchar（锡尔查尔国家技术学院）
Online Social Networks have embarked on the importance of connection strength measures which has a broad array of applications such as, analyzing diffusion behaviors, community detection, link predictions, recommender systems. Though there are some existing connection strength measures, the density that a connection shares with it's neighbors and the directionality aspect has not received much attention. In this paper, we have proposed an asymmetric edge similarity measure namely, Neighborhood Density-based Edge Similarity (NDES) which provides a fundamental support to derive the strength of c…
As an increasing number of social networking data is published and shared for commercial and research purposes, privacy issues about the individuals in social networks have become serious concerns. Vertex identification, which identifies a particular user from a network based on background knowledge such as vertex degree, is one of the most important problems that has been addressed. In reality, however, each individual in a social network is inclined to be associated with not only a vertex identity but also a community identity, which can represent the personal privacy information sensitive t…
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 …
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 in…
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the literature followed by general principles behind the optimal procedures that lead to minimax estimation and testing. This allows us to connect problems in network analysis to other statistical inference problems from a general perspective.
Huawei Noah's Ark Lab（华为诺亚方舟实验室）；University of South Florida（南佛罗里达大学）；University of Michigan（密歇根大学）；GIPSA-lab, University Grenoble-Alpes（格勒诺布尔-阿尔卑斯大学GIPSA实验室）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communities. We make use of a variational Bayes approach for jointly inferring the shared and unshared hidden communities from multilayer network observations. We show that our approach outperforms state-of-the-art algorithms in detecting disparate (shared and private) communities on synthetic data as well…
Discovery of communities in complex networks is a topic of considerable recent interest within the complex systems community. Due to the dynamic and rapidly evolving nature of large-scale networks, like online social networks, the notion of stronger local and global interactions among the nodes in communities has become harder to capture. In this paper, we present a novel graphical inference method - GI-OHMS (Graphical Inference in Observed-Hidden variable Merged Seeded network) to solve the problem of overlapping community detection. The novelty of our approach is in transforming the complex …
University of California, Irvine（加州大学欧文分校）；Princeton University（普林斯顿大学）；Microsoft Research, New England（微软研究院新英格兰分院）
Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced by Airoldi et al. This model allows for nodes to have fractional memberships in multiple communities and assumes that the community membershi…
