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 for mixed membership community detection. Especially, Mixed-ISC provides satisfactory performances on weak signal networks.
Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models
Graduate School of Systems Design, Tokyo Metropolitan University（东京 Metropolitan 大学系统设计研究生院）；Principles of Informatics Research Division, National Institute of Informatics（国家信息研究所信息原理研究部门）
Community detection is a well established method for studying the meso scale structure of social networks. Applying a community detection algorithm results in a division of a network into communities that is often used to inspect and reason about community membership of specific nodes. This micro level interpretation step of community structure is a crucial step in typical social science research. However, the methodological caveat in this step is that virtually all modern community detection methods are non-deterministic and based on randomization and approximated results. This needs to be ex…
A central aim of modeling complex networks is to accurately embed networks in order to detect structures and predict link and node properties. The latent space models (LSM) have become prominent frameworks for embedding networks and include the latent distance (LDM) and eigenmodel (LEM) as the most widely used LSM specifications. For latent community detection, the embedding space in LDMs has been endowed with a clustering model whereas LEMs have been constrained to part-based non-negative matrix factorization (NMF) inspired representations promoting community discovery. We presently reconcile…
Mixed-SCORE is a recent approach for mixed membership community detection proposed by Jin et al. (2017) which is an extension of SCORE (Jin, 2015). In the note Jin et al. (2018), the authors propose SCORE+ as an improvement of SCORE to handle with weak signal networks. In this paper, we propose a method called Mixed-SCORE+ designed based on the Mixed-SCORE and SCORE+, therefore Mixed-SCORE+ inherits nice properties of both Mixed-SCORE and SCORE+. In the proposed method, we consider K+1 eigenvectors when there are K communities to detect weak signal networks. And we also construct vertices hunt…
The importance of peer influence on consumer actions plays a vital role in marketing efforts. However, peer influence effects are often confounded with latent homophily, which are unobserved commonalities that drive friendship. Understanding causality has become one of the pressing issues of current research. We present an approach to explicitly account for various causal influences. We implement a simulation framework to show the effectiveness of two latent homophily proxies, latent coordinates and community membership, in improving peer influence effect estimates on game downloads in a Japan…
University of California, Irvine（加州大学欧文分校）；University of Southern California（南加州大学）
Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform hypergraph consisting of (user, tag, resource) hyperedges. We posit a probabilistic mixed membership community model, and prove that the tensor method consistently learns the communities under efficient sample complexit…
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…
China University of Mining and Technology（中国矿业大学）；Nankai University（南开大学）
Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) based on the regularized Laplacian matrix. Mixed-RSC is designed based on an ideal cone structure of the variant for the eigen-decomposition of the population regularized Laplacian matrix. We show that the algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vector of each node. As a byproduc…
We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require strong assumptions about the population, are computationally expensive, and only provide an overall error bound for the whole community membership matrix. This paper provides uniform rates of convergence for the inferred community membership vector of each node in a network generated from the Mixed Membership Stochastic Blockmodel (MMSB); to our knowledge, thi…
Nowadays, detecting anomalous communities in networks is an essential task in research, as it helps discover insights into community-structured networks. Most of the existing methods leverage either information regarding attributes of vertices or the topological structure of communities. In this study, we introduce the Co-Membership-based Generic Anomalous Communities Detection Algorithm (referred as to CMMAC), a novel and generic method that utilizes the information of vertices co-membership in multiple communities. CMMAC is domain-free and almost unaffected by communities' sizes and densitie…
University of Alberta（阿尔伯塔大学）；University of New South Wales（新南威尔士大学）；University of Social Sciences, Poland（波兰社会科学大学）
The Mixed-Membership Stochastic Blockmodel~(MMSB) is proposed as one of the state-of-the-art Bayesian relational methods suitable for learning the complex hidden structure underlying the network data. However, the current formulation of MMSB suffers from the following two issues: (1), the prior information~(e.g. entities' community structural information) can not be well embedded in the modelling; (2), community evolution can not be well described in the literature. Therefore, we propose a non-parametric fragmentation coagulation based Mixed Membership Stochastic Blockmodel (fcMMSB). Our model…
Most real-world social networks are inherently dynamic, composed of communities that are constantly changing in membership. To track these evolving communities, we need dynamic community detection techniques. This article evaluates the performance of a set of game theoretic approaches for identifying communities in dynamic networks. Our method, D-GT (Dynamic Game Theoretic community detection), models each network node as a rational agent who periodically plays a community membership game with its neighbors. During game play, nodes seek to maximize their local utility by joining or leaving the…
Community Discovery in complex networks is the problem of detecting, for each node of the network, its membership to one of more groups of nodes, the communities, that are densely connected, or highly interactive, or, more in general, similar, according to a similarity function. So far, the problem has been widely studied in monodimensional networks, i.e. networks where only one connection between two entities can exist. However, real networks are often multidimensional, i.e., multiple connections between any two nodes can exist, either reflecting different kinds of relationships, or represent…
Stream graphs are a very useful mode of representation for temporal network data, whose richness offers a wide range of possible approaches. The various methods aimed at generalising the classical approaches applied to static networks are constantly being improved. In this paper, we describe a framework that extend to stream graphs iterative weighted-rich-clubs characterisation for static networks proposed in [1]. The general principle is that we no longer consider the membership of a node to one of the weighted-rich-clubs for the whole time period, but each node is associated with a temporal …
In this work, we explore four common algorithms for community detection in networks, namely Agglomerative Hierarchical Clustering, Divisive Hierarchical Clustering (Girvan-Newman), Fastgreedy and the Louvain Method. We investigate their mechanics and compare their differences in terms of implementation and results of the clustering behavior on a standard dataset. We further propose some enhancements to these algorithms that show promising results in our evaluations, such as self-neighboring for Neighbor Matrix constructions, a deterministic slightly faster version of the Louvain Method that fa…
University of Maryland, College Park（马里兰大学帕克分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on sparse node membership vectors. Our algorithm is based on sparse principal subspace estimation with iterative thresholding. The method is computationally efficient, with a computational cost equivalent to estimating the leading eigenvectors of the adjacency matrix, and does not require an additional clustering step, unlike spectral clustering methods. We show th…
This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly interconnected dynamical entities. Complex networks like real networks can also have community structure. There are several types of methods and algorithms for detection and identification of communities in complex networks. Several complex networks have the property of clustering or network transitivity. Some of the important concepts in the field of complex network…
Advanced Digital Sciences Center（高级数字科学中心）；The University of Queensland（昆士兰大学）；Zhejiang University City College（浙江大学城市学院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Most existing community-related studies focus on detection, which aim to find the community membership for each user from user friendship links. However, membership alone, without a complete profile of what a community is and how it interacts with other communities, has limited applications. This motivates us to consider systematically profiling the communities and thereby developing useful community-level applications. In this paper, we for the first time formalize the concept of community profiling. With rich user information on the network, such as user published content and user diffusion …
Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community structure, while ensembles with high assortativity are much less biased towards clustering or community structure. Further, clustered networks can amplify small homophilic bias for trait assortativity. This marked asymmetry suggests that transitivity, rather than homophily, drives the standard nonsocial/social network dichotomy.
Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network science. Community detection aims to partition the network into sets of nodes that are densely connected internally but sparsely connected to other dense sets of nodes. Current work on community detection mostly focuses on static networks. However, many real world networks are dynamic, i.e. their structure and properties change with time, requiring methods for …
A recent article proposed reduced mutual information for evaluation of clustering, classification and community detection. The motivation is that the standard normalized mutual information (NMI) may give counter-intuitive answers under certain conditions and particularly when the number of clusters differs between the two divisions under consideration. The motivation makes sense. However, the examples given in the article are not accurate, and this comment discusses why. In addition, this comment also empirically demonstrates that the reduced mutual information cannot handle the difficulties o…
We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link-usage optimally. We propose weighting networks using these expected link-usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks.
SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership e…
Performing analytic of household load curves (LCs) has significant value in predicting individual electricity consumption patterns, and hence facilitate developing demand-response strategy, and finally achieve energy efficiency improvement and emission reduction. LC clustering is a widely used analytic technology, which discovers electricity consumption patterns by grouping similar LCs into same sub-groups. However, previous clustering methods treat each LC in the data set as an individual time series, ignoring the inherent relationship among different LCs, restraining the performance of the c…
Detecting communities in large-scale networks is a challenging task when each vertex may belong to multiple communities, as is often the case in social networks. The multiple memberships of vertices and thus the strong overlaps among communities render many detection algorithms invalid. We develop a Partial Community Merger Algorithm (PCMA) for detecting communities with significant overlaps as well as slightly overlapping and disjoint ones. It is a bottom-up approach based on properly reassembling partial information of communities revealed in ego networks of vertices to reconstruct complete …
China University of Mining and Technology（中国矿业大学）；Nankai University（南开大学）
Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized graph Laplacian matrix and then employ it to three classical spectral clustering approaches under the degree-corrected stochastic block model. If the number of communities is known as $K$, we consider more than $K$ leading eigenvectors and weight them by their corresponding eigenvalues in the spectral clustering procedure to improve the performance. Three improv…
The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-free but fails to provide quality assurance for the detected communities. In this paper, we propose a novel unified framework to combine the advantages of these two principles. The presented method, SGC-GEN, not only considers the detection error caused by the corresponding model mi…
Like clustering analysis, community detection aims at assigning nodes in a network into different communities. Fdp is a recently proposed density-based clustering algorithm which does not need the number of clusters as prior input and the result is insensitive to its parameter. However, Fdp cannot be directly applied to community detection due to its inability to recognize the community centers in the network. To solve the problem, a new community detection method (named IsoFdp) is proposed in this paper. First, we use Isomap technique to map the network data into a low dimensional manifold wh…
Nordita（北欧理论物理研究所）；Stockholm University（斯德哥尔摩大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）；Harvard University（哈佛大学）
Recently, in many systems such as speech recognition and visual processing, deep learning has been widely implemented. In this research, we are exploring the possibility of using deep learning in community detection among the graph datasets. Graphs have gained growing traction in different fields, including social networks, information graphs, the recommender system, and also life sciences. In this paper, we propose a method of community detection clustering the nodes of various graph datasets. We cluster different category datasets that belong to Affiliation networks, Animal networks, Human c…
National Taiwan University（台湾大学）；Mila-Quebec Institute for Learning Algorithms（Mila-魁北克学习算法研究所）；Harvard University（哈佛大学）；Element AI；HEC Montreal（蒙特利尔高等商学院）
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both…
Random graph models are important constructs for data analytic applications as well as pure mathematical developments, as they provide capabilities for network synthesis and principled analysis. Several models have been developed with the aim of faithfully preserving important graph metrics and substructures. With the goal of capturing degree distribution, clustering coefficient, and communities in a single random graph model, we propose a new model to address shortcomings in a progression of network modeling capabilities. The Block Two-Level Erd{ő}s-R{é}nyi (BTER) model of Seshadhri et al., d…
One of the main organizing principles in real-world social, information and technological networks is that of network communities, where sets of nodes organize into densely linked clusters. Even though detection of such communities is of great interest, understanding the structure communities in large networks remains relatively limited. Due to unavailability of labeled ground-truth data it is practically impossible to evaluate and compare different models and notions of communities on a large scale. In this paper we identify 6 large social, collaboration, and information networks where nodes …
KTH Royal Institute of Technology（KTH皇家理工学院）；University of Science and Technology of China（中国科学技术大学）
Social networks are often modeled using signed graphs, where vertices correspond to users and edges have a sign that indicates whether an interaction between users was positive or negative. The arising signed graphs typically contain a clear community structure in the sense that the graph can be partitioned into a small number of polarized communities, each defining a sparse cut and indivisible into smaller polarized sub-communities. We provide a local clustering oracle for signed graphs with such a clear community structure, that can answer membership queries, i.e., "Given a vertex $v$, which…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced cluster sizes. Our approach parameterizes a family of graphs by adaptively modulatin…
Discovering overlapping community structures is a crucial step to understanding the structure and dynamics of many networks. In this paper we develop a symmetric binary matrix factorization model (SBMF) to identify overlapping communities. Our model allows us not only to assign community memberships explicitly to nodes, but also to distinguish outliers from overlapping nodes. In addition, we propose a modified partition density to evaluate the quality of community structures. We use this to determine the most appropriate number of communities. We evaluate our methods using both synthetic bench…
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…
Finding Common Ground: Graded Communal Knowledge in Bluesky Starter Packs
Northeastern University（东北大学）；Boston Children’s Hospital（波士顿儿童医院）；University of Maryland, College Park（马里兰大学帕克分校）；University of Virginia（弗吉尼亚大学）；University of Vermont（佛蒙特大学）
Institute of Mathematics and Computer Science, University of São Paulo（圣保罗大学数学与计算机科学学院）；Department of Computing and Mathematics, University of São Paulo（圣保罗大学计算与数学系）
In this paper, we propose a technique for time series clustering using community detection in complex networks. Firstly, we present a method to transform a set of time series into a network using different distance functions, where each time series is represented by a vertex and the most similar ones are connected. Then, we apply community detection algorithms to identify groups of strongly connected vertices (called a community) and, consequently, identify time series clusters. Still in this paper, we make a comprehensive analysis on the influence of various combinations of time series distan…
Michigan State University（密歇根州立大学）；NEC Laboratories America（美国 NEC 实验室）
This paper addresses the problem of community detection in networked data that combines link and content analysis. Most existing work combines link and content information by a generative model. There are two major shortcomings with the existing approaches. First, they assume that the probability of creating a link between two nodes is determined only by the community memberships of the nodes; however other factors (e.g. popularity) could also affect the link pattern. Second, they use generative models to model the content of individual nodes, whereas these generative models are vulnerable to …
