In this paper we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describe relationships between two types of nodes. Our method improves performance by recognizing the distinction between two types of missing edges---ones among the nodes in each node type and the others between two node types. Our method can also explicitly assign community membership and distinguish outliers from overlapping nodes, as well as incorporating existing knowledge on the network. We propose a generalized partition density for bipartite networks as a quality function, which identifies the most appropriate number of communities. The experimental results on both synthetic and real-world networks demonstrate the effectiveness of our method.
Community detection in complex networks is a topic of high interest in many fields. Bipartite networks are a special type of complex networks in which nodes are decomposed into two disjoint sets, and only nodes between the two sets can be connected. Bipartite networks represent diverse interaction patterns in many real-world systems, such as predator-prey networks, plant-pollinator networks, and drug-target networks. While community detection in unipartite networks has been extensively studied in the past decade, identification of modules or communities in bipartite networks is still in its ea…
This paper introduces a computationally inexpensive method of extracting the backbone of one-mode networks projected from bipartite networks. We show that the edge weights in the one-mode projections are distributed according to a Poisson binomial distribution and that finding the expected weight distribution of a one-mode network projected from a random bipartite network only requires knowledge of the bipartite degree distributions. Being able to extract the backbone of a projection is highly beneficial in filtering out redundant information in large complex networks and narrowing down the in…
Community structures detection in signed network is very important for understanding not only the topology structures of signed networks, but also the functions of them, such as information diffusion, epidemic spreading, etc. In this paper, we develop a joint nonnegative matrix factorization model to detect community structures. In addition, we propose modified partition density to evaluate the quality of community structures. We use it to determine the appropriate number of communities. The effectiveness of our approach is demonstrated based on both synthetic and real-world networks.
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…
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or two-mode networks. We propose two generative models that can be easily tuned to reproduce the characteristics of real-world networks, not just qualitatively, but quantitatively. The characteristics we consider are the degree distributions and the metamorphosis coefficient. The metamorphosis coefficient, a bipartite analogue of the clustering coefficient, is the pro…
Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest in small-scale structures, shorter timescales may be better. However, current methods for analyzing networks at different timescales require expensive and often infeasible network reconstructions. To overcome this problem, we introduce a method that takes advantage of the inner-workings of the map equation and evades the reconstruction step. This makes it pos…
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, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and …
The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities.
This paper investigates community detection by modularity maximisation on bipartite networks. In particular we are interested in how the operation of projection, using one node set of the bipartite network to infer connections between nodes in the other set, interacts with community detection. We first define a notion of modularity appropriate for a projected bipartite network and outline an algorithm for maximising it in order to partition the network. Using both real and synthetic networks we compare the communities found by five different algorithms, where each algorithm maximises a differe…
Bipartite networks are powerful descriptions of complex systems characterized by two different classes of nodes and connections allowed only across but not within the two classes. Surprisingly, current complex network theory presents a theoretical bottle-neck: a general framework for local-based link prediction directly in the bipartite domain is missing. Here, we overcome this theoretical obstacle and present a formal definition of common neighbour index (CN) and local-community-paradigm (LCP) for bipartite networks. As a consequence, we are able to introduce the first node-neighbourhood-base…
Local community detection consists of finding a group of nodes closely related to the seeds, a small set of nodes of interest. Such group of nodes are densely connected or have a high probability of being connected internally than their connections to other clusters in the network. Existing local community detection methods focus on finding either one local community that all seeds are most likely to be in or finding a single community for each of the seeds. However, a seed member usually belongs to multiple local overlapping communities. In this work, we present a novel method of detecting mu…
Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite network consists of one set of nodes and a bipartite network consists of two nonoverlapping sets of nodes with only links joining the nodes in different sets. However, a third type of network exists, defined here as the mixture network. Just like a bipartite network, a mixture network also consists of two sets of nodes, but some nodes may simultaneously belong to…
Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for simplicity's sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a single type of node. When it comes to mesoscale structures such as communities, however, properly incorporating a priori structural restrictions such as bipartivity is ever more important. In this paper, as a case study, we take the community structure of bipartite networks in various scales to examine the amount of information of bipartivity encoded in the commu…
University of Colorado（科罗拉多大学）；BioFrontiers Institute（生物前沿研究所）
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), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in…
Community search over bipartite graphs has attracted significant interest recently. In many applications such as user-item bipartite graph in E-commerce, customer-movie bipartite graph in movie rating website, nodes tend to have attributes, while previous community search algorithm on bipartite graphs ignore attributes, which makes the returned results with poor cohesion with respect to their node attributes. In this paper, we study the community search problem on attributed bipartite graphs. Given a query vertex q, we aim to find attributed $\left(α,β\right)$-communities of $G$, where the str…
Community structures detection is one of the fundamental problems in complex network analysis towards understanding the topology structures of the network and the functions of it. Nonnegative matrix factorization (NMF) is a widely used method for community detection, and modularity Q and modularity density D are criteria to evaluate the quality of community structures. In this paper, we establish the connections between Q, D and NMF for the first time. Q maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when $n$ is large, and D maximizati…
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 discovery is an important task for graph mining. Owing to the nonstructure, the high dimensionality, and the sparsity of graph data, it is not easy to obtain an appropriate community partition. In this paper, a deep graph convolution neural network with non-negative matrix factorization (DGCN-NMF) is proposed for community discovery. DGCN-NMF employs multiple graph convolution layers to obtain the low dimensional embedding. In each layer, the last output and the non-negative matrix factorization's results of the previous outputs are inputted into the current layer. The community part…
Mapping network flows provides insight into the organization of networks, but even though many real-networks are bipartite, no method for mapping flows takes advantage of the bipartite structure. What do we miss by discarding this information and how can we use it to understand the structure of bipartite networks better? The map equation models network flows with a random walk and exploits the information-theoretic duality between compression and finding regularities to detect communities in networks. However, it does not use the fact that random walks in bipartite networks alternate between n…
The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-…
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 is a fundamental and critical characteristic of a Large-scale Undirected Network (LUN) like a social network, making community detection a vital yet thorny issue in LUN representation learning. Owing to its good scalability and interpretability, a Symmetric and Nonnegative Matrix Factorization (SNMF) model is commonly used to tackle this issue. However, it adopts a unique Latent Factor (LF) matrix for precisely representing an LUN's symmetry, which leads to a reduced LF space that impairs its representational learning ability. Motivated by this discovery, this study proposes a Symmet…
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…
WCCS: Efficient Wedge Conductance Community Search over Large Temporal Bipartite Graphs (Full Paper)
College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Huazhong University of Science and Technology（华中科技大学）；Beijing Institute of Technology（北京理工大学）
College of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院）；Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences（中国科学院重庆绿色智能技术研究院）；College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）
Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF) model is frequently adopted to address this issue owing to its great interpretability and scalability. However, it adopts a single latent factor matrix to represent an undirected network for precisely representing its symmetry, which leads to loss of representation learning ability due to the reduced latent space. Motivated by this discovery, this paper proposes…
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 communities in the bipartite setting, in addition to node covariates with information about the matching. We derive a simple fast algorithm for fitting the model based on variational inference ideas and show its effectiveness on both simulated and real data. A variation of the model to allow for degree-correction is also considered, in addition to a novel ap…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；Google（谷歌）
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a low-dimensional vector representation (the embedding) for each node. Despite the widespread use of these embeddings for a variety of downstream transductive machine learning tasks, there is little principled analysis of the effectiveness of this approach for common tasks. In this work, we provide an empirical and theoretical analysis for the performance of a class o…
Community structures detection in complex network is important for understanding not only the topological structures of the network, but also the functions of it. Stochastic block model and nonnegative matrix factorization are two widely used methods for community detection, which are proposed from different perspectives. In this paper, the relations between them are studied. The logarithm of likelihood function for stochastic block model can be reformulated under the framework of nonnegative matrix factorization. Besides the model equivalence, the algorithms employed by the two methods are di…
Multilayer networks or MLNs (also called multiplexes or network of networks) are being used extensively for modeling and analysis of data sets with multiple entity and feature types as well as their relationships. As the concept of communities and hubs are used for these analysis, a structure-preserving definition for them on MLNs (that retains the original MLN structure and node/edge labels and types) and its efficient detection are critical. There is no structure-preserving definition of a community for a MLN as most of the current analyses aggregate a MLN to a single graph. Although there i…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm in the reduced spectral domain. We focus on the adjacency-based spectral clustering and for the first step, propose a new data-driven regularization that can restore the concentration of the adjacency matrix even for the sparse networks. This result is based on recent work on re…
The world around us consists of objects that have different relationships with each other. The result of these communications is various networks, part of which are bipartite networks. While many studies have investigated essential network members, less attention has been paid to the bipartite graphs. On the other hand, one of the most critical aspects of network analysis is the detection and extraction of communities that arise in the structure of networks. For these reasons, we have introduced a measure called H.H to identify influential nodes in community formation in the one-mode projectio…
We investigate the formation of musical preferences of millions of users of the NetEase Cloud Music (NCM), one of the largest online music platforms in China. We combine the methods from complex networks theory and information sciences within the context of Big Data analysis to unveil statistical patterns and community structures underlying the formation and evolution of musical preference behaviors. Our analyses address the decay patterns of music influence, users' sensitivity to music, age and gender differences, and their relationship to regional economic indicators. Employing community det…
Detecting whether a news article is fake or genuine is a crucial task in today's digital world where it's easy to create and spread a misleading news article. This is especially true of news stories shared on social media since they don't undergo any stringent journalistic checking associated with main stream media. Given the inherent human tendency to share information with their social connections at a mouse-click, fake news articles masquerading as real ones, tend to spread widely and virally. The presence of echo chambers (people sharing same beliefs) in social networks, only adds to this …
Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clu…
Bipartite user-object networks are becoming increasingly popular in representing user interaction data in a web or e-commerce environment. They have certain characteristics and challenges that differentiates them from other bipartite networks. This paper analyzes the properties of five real world user-object networks. In all cases we found a heavy tail object degree distribution with popular objects connecting together a large part of the users causing significant edge inflation in the projected users network. We propose a novel edge weighting strategy based on tf-idf and show that the new sch…
Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. When this side information is in the form of item-item correlation matrices or graphs, existing CMTF algorithms may fall short. Alleviating current limitations, we introduce a novel model coined coupled graph-tensor factorization (CGTF) that judiciously accounts for graph-related…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should guarantee the stability even under some information loss. With six bipartite networks, we investigate the stabilities of fifteen similarity measurements by comparing the similarity matrixes of two data samples which are randomly divided from original data sets. Results show that, the fifteen measurements can be well classified into three clusters according to …
For a given graph, $G$, let $A$ be the adjacency matrix, $D$ is the diagonal matrix of degrees, $L' = D - A$ is the combinatorial Laplacian, and $L = D^{-1/2}L'D^{-1/2}$ is the normalized Laplacian. Recently, the eigenvectors corresponding to the smallest eigenvalues of $L$ and $L'$ have been of great interest because of their application to community detection, which is a nebulously defined problem that essentially seeks to find a vertex set $S$ such that there are few edges incident with exactly one vertex of $S$. The connection between community detection and the second smallest eigenvalue …
An important step in unveiling the relation between network structure and dynamics defined on networks is to detect communities, and numerous methods have been developed separately to identify community structure in different classes of networks, such as unipartite networks, bipartite networks, and directed networks. We show that both unipartite and directed networks can be represented as bipartite networks, and their modularity is completely consistent with that for bipartite networks, the detection of modular structure on which can be reformulated as modularity maximization. To optimize the …
A common form of competition is one where judges grade contestants' performances which are then compiled to determine the final ranking of the contestants. Unlike in another common form of competition where two contestants play a head-to-head match to produce a winner as in football or basketball, the objectivity of judges are prone to be questioned, potentially undermining the public's trust in the fairness of the competition. In this work we show, by modeling the judge--contestant competition as a weighted bipartite network, how we can identify biased scores and measure their impact on our i…
Random-walk based network embedding algorithms like DeepWalk and node2vec are widely used to obtain Euclidean representation of the nodes in a network prior to performing downstream inference tasks. However, despite their impressive empirical performance, there is a lack of theoretical results explaining their large-sample behavior. In this paper, we study node2vec and DeepWalk through the perspective of matrix factorization. In particular, we analyze these algorithms in the setting of community detection for stochastic blockmodel graphs (and their degree-corrected variants). By exploiting the…
We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert, and Kumara, but is able to detect communities that overlap. Like the original algorithm, vertices have labels that propagate between neighbouring vertices so that members of a community reach a consensus on their community membership. Our main contribution is to extend the label and propagation step to include information about more than one community: each vertex can now belong to up to v communities, where v is the paramete…
Institute of Computer Science, Polish Academy of Sciences（波兰科学院计算机科学研究所）
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters.We adapt the advances of last decade in unipartite complex networks modeling to the bigraph setting. This data structure can be observed in several situations. However, only a few datasets are freely available to test the algorithms (e.g. community detection, influential nodes identification, information retrieval) which operate on such data. Therefore…
Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and time-varying community detection in time-evolving graph sequences. The matrix factorization model allows the user to home in on and display interesting, underlying structure and its evolution over time. The methods are scalable to weighted networks with a large number of time points or nodes, and can accommodate sudden changes to graph topology. Our techniques ar…
