Community Structure In Bipartite Networks Research Articles

A spectral method of modularity for community detection in bipartite networks

Community detection in bipartite networks is a popular topic. Two widely used methods to capture community structures in bipartite networks are the method of modularity and the method of graph partitioning. Our analytical results show that the modularity maximization problem can be reformulated as a spectral problem after relaxing the discreteness constraints. This means that the method of modularity and the method of graph partitioning are essentially equivalent. As an application, a spectral algorithm of modularity is devised for identifying community structures in bipartite networks. Experimental results on synthetic networks and real-world networks indicate that our algorithm performs better than those algorithms of modularity local maximization, such as BRIM (bipartite recursively induced moduls) and bLP (bipartite label propagation). Therefore, our results shed light on the methods of community detection in bipartite networks.

BiNeTClus

We investigate the problem of community detection in bipartite networks that are characterized by the presence of two types of nodes such that connections exist only between nodes of different types. While some approaches have been proposed to identify community structures in bipartite networks, there are a number of problems still to solve. In fact, the majority of the proposed approaches suffer from one or even more of the following limitations: (1) difficulty in detecting communities in the presence of many non-discriminating nodes with atypical connections that hide the community structures, (2) loss of relevant topological information due to the transformation of the bipartite network to standard plain graphs, and (3) manually specifying several input parameters, including the number of communities to be identified. To alleviate these problems, we propose BiNeTClus, a parameter-free community detection algorithm in bipartite networks that operates in two phases. The first phase focuses on identifying an initial grouping of nodes through a transactional data model capable of dealing with the situation that involves networks with many atypical connections, that is, sparsely connected nodes and nodes of one type that massively connect to all other nodes of the second type. The second phase aims to refine the clustering results of the first phase via an optimization strategy of the bipartite modularity to identify the final community structures. Our experiments on both synthetic and real networks illustrate the suitability of the proposed approach.

Community detection by enhancing community structure in bipartite networks

Community detection is one of the primary tools to discover useful information that is hidden in complex networks. Some community detection algorithms for bipartite networks have been proposed from various viewpoints. However, the performance of these algorithms deteriorates when the community structure becomes unclear. Enhancing community structure remains a nontrivial task. In this paper, we propose a community detection algorithm, called ECD, that enhances community structure in bipartite networks. In the proposed ECD, the topology of a network is modified by reducing unnecessary edges that are connected to neighboring low-weight communities. Therefore, an ambiguous community structure is converted into a structure that is much clearer than the original structure. The experimental results on both artificial and real-world networks verify the accuracy and reliability of our algorithm. Compared with existing community detection algorithms using state-of-the-art methods, our algorithm has better performance.

Overlapping Community Detecting Based on Complete Bipartite Graphs in Micro-Bipartite Network Bi-Egonet

Community detection has become a hot topic in complex networks. It plays an important role in information recommendation and public opinion control. Bipartite network, as a special complex network, reflects the characteristics of a kind of network in our life truly and objectively. Therefore, detecting community structure in bipartite networks is of great significance and has practical value. In this paper, we first introduce two concepts: a) a micro-bipartite network model Bi-EgoNet which can be used to analyze bipartite network from a micro view to reduce the complexity of structure in bipartite networks, and b) a complete bipartite graph that is a special bipartite graph with the indivisible property. Then, we propose a novel overlapping community detection algorithm based on a complete bipartite graph in micro-bipartite network Bi-EgoNet (CBG&BEN), which combines advantages of both a complete bipartite graph and Bi-EgoNet to get an optimal community structure. The CBG&BEN is evaluated on accuracy and effectiveness in several synthetic and real-world bipartite networks. The CBG&BEN is compared with other excellent existing algorithms, and our experimental results demonstrated that CBG&BEN is better at detecting overlapping community structure in bipartite networks.

Community detection based on preferred mode in bipartite networks

Identifying community structures in bipartite networks is a popular topic. People usually focus on one of two modes in bipartite networks when uncovering their community structures. According to this understanding, we design a community detection algorithm based on preferred mode in bipartite networks. This algorithm can select corresponding preferred mode according to specific application scenario and effectively extract community information in bipartite networks. The trials in artificial and real-world networks show that the algorithm based on preferred mode has better performances in both small size of bipartite networks and large size of bipartite networks.

A comparative study of the measures for evaluating community structure in bipartite networks

The community structure is an elementary property of complex networks. In bipartite networks, various global measures have been proposed to evaluate the quality of communities. However, few studies focus on comparing the performance of those measures on benchmark networks. Therefore, in this paper, we first propose a memetic algorithm (MACD-BNs) to detect communities in bipartite networks and then use it to separately optimize four existing measures to compare the performance of these measures. These four measures that belong to the same class are based on the idea that the same type nodes are grouped into a community due to their similar link patterns. Experimental results on some real-life and synthetic networks illustrate the effectiveness of the MACD-BNs. The comparison among different measures answers which of the four measures has the best relative performance in most cases and exposes the limitations of some measures.

A novel community detection method in bipartite networks

Community structure is a common and important feature in many complex networks, including bipartite networks, which are used as a standard model for many empirical networks comprised of two types of nodes. In this paper, we propose a two-stage method for detecting community structure in bipartite networks. Firstly, we extend the widely-used Louvain algorithm to bipartite networks. The effectiveness and efficiency of the Louvain algorithm have been proved by many applications. However, there lacks a Louvain-like algorithm specially modified for bipartite networks. Based on bipartite modularity, a measure that extends unipartite modularity and that quantifies the strength of partitions in bipartite networks, we fill the gap by developing the Bi-Louvain algorithm that iteratively groups the nodes in each part by turns. This algorithm in bipartite networks often produces a balanced network structure with equal numbers of two types of nodes. Secondly, for the balanced network yielded by the first algorithm, we use an agglomerative clustering method to further cluster the network. We demonstrate that the calculation of the gain of modularity of each aggregation, and the operation of joining two communities can be compactly calculated by matrix operations for all pairs of communities simultaneously. At last, a complete hierarchical community structure is unfolded. We apply our method to two benchmark data sets and a large-scale data set from an e-commerce company, showing that it effectively identifies community structure in bipartite networks.

Detecting one-mode communities in bipartite networks by bipartite clustering triangular

In this paper, an algorithm is proposed to detect one-mode community structures in bipartite networks, and to deduce which one-mode community structures are weighted. After analyzing the topological properties in bipartite networks, bipartite clustering triangular is introduced. First, bipartite networks are projected into two weighted one-mode networks by bipartite clustering triangular. Then all the maximal sub-graphs from two one-mode weighted networks are extracted and the maximal sub-graphs are merged together using a weighted clustering threshold. In addition, the proposed algorithm successfully finds overlapping vertices between one-mode communities. Experimental results using some real-world network data shows that the performance of the proposed algorithm is satisfactory.

Density-based modularity for evaluating community structure in bipartite networks

A bipartite network is an important type of complex network in human social activities. Newman defined modularity as a measurement for evaluating community structure in unipartite networks. Due to the success of modularity in unipartite networks, bipartite modularities were developed according to different understandings of community in bipartite networks. However, these modularity measurements are subject to resolution limits that could reduce the quality of community partitioning. These modularity measurements contain an intrinsic scale that depends on the total size of links and ignores the number of nodes in a bipartite network. In this paper, we first illustrate such resolution limits of traditional bipartite modularities using several examples of bipartite networks. Next, we propose a quantitative measurement called density-based modularity to evaluate community partitioning in bipartite networks. We verify that optimization of the density-based modularity proposed has no resolution limit. By optimizing this density-based modularity, we can partition the network into the appropriate communities. Experiments on synthetic and real-world bipartite networks verify the accuracy and reliability of our bipartite density-based modularity.

Detecting Communities in 2-Mode Networks via Fast Nonnegative Matrix Trifactorization

With the rapid development of the Internet and communication technologies, a large number of multitype relational networks widely emerge in real world applications. The bipartite network is one representative and important kind of complex networks. Detecting community structure in bipartite networks is crucial to obtain a better understanding of the network structures and functions. Traditional nonnegative matrix factorization methods usually focus on homogeneous networks, and they are subject to several problems such as slow convergence and large computation. It is challenging to effectively integrate the network information of multiple dimensions in order to discover the hidden community structure underlying heterogeneous interactions. In this work, we present a novel fast nonnegative matrix trifactorization (F-NMTF) method to cocluster the 2-mode nodes in bipartite networks. By constructing the affinity matrices of 2-mode nodes as manifold regularizations of NMTF, we manage to incorporate the intratype and intratype information of 2-mode nodes to reveal the latent community structure in bipartite networks. Moreover, we decompose the NMTF problem into two subproblems, which are involved with much less matrix multiplications and achieve faster convergence. Experimental results on synthetic and real bipartite networks show that the proposed method improves the slow convergence of NMTF and achieves high accuracy and stability on the results of community detection.

Modularity Density for Evaluating Community Structure in Bipartite Networks

Modularity Density for Evaluating Community Structure in Bipartite Networks

Efficiently inferring community structure in bipartite networks.

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 may be trivially extended to k-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this model's ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.

Community structures in bipartite networks: a dual-projection approach.

Identifying communities or clusters in networked systems has received much attention across the physical and social sciences. Most of this work focuses on single layer or one-mode networks, including social networks between people or hyperlinks between websites. Multilayer or multi-mode networks, such as affiliation networks linking people to organizations, receive much less attention in this literature. Common strategies for discovering the community structure of multi-mode networks identify the communities of each mode simultaneously. Here I show that this combined approach is ineffective at discovering community structures when there are an unequal number of communities between the modes of a multi-mode network. I propose a dual-projection alternative for detecting communities in multi-mode networks that overcomes this shortcoming. The evaluation of synthetic networks with known community structures reveals that the dual-projection approach outperforms the combined approach when there are a different number of communities in the various modes. At the same time, results show that the dual-projection approach is as effective as the combined strategy when the number of communities is the same between the modes.

Uncovering overlapping community structures by the key bi-community and intimate degree in bipartite networks

Although many successful algorithms have been designed to discover community structures in network, most of them are dedicated to disjoint and non-overlapping communities. Very few of them are intended to discover overlapping communities, particularly the detection of such communities have hardly been explored in the bipartite networks. In this paper, a novel algorithm is proposed to detect overlapping community structures in bipartite networks. After analyzing the topological properties in bipartite networks, the key bi-communities and free-nodes are introduced. Firstly, some key bi-communities and free-nodes are extracted from the original bipartite networks. Then the free-nodes are allocated into a certain key bi-community by some given rules. In addition, the proposed algorithm successfully finds overlapping vertices between communities. Experimental results using some real-world networks data show that the performance of the proposed algorithm is satisfactory.

Detecting community structure in bipartite networks based on matrix factorisation

Community detection in bipartite network is very important in the research on the theory and applications of complex network analysis. In this paper, an algorithm for detecting community structure in bipartite networks based on matrix factorisation is presented. The algorithm first partitions the network into two parts, each of which can reserve the community information as much as possible, and then the two parts are further recursively partitioned until the modularity cannot be further improved. While partitioning the network, we use the approach of matrix decomposition so that the row space of the associated matrix of the networks can be approximated as close as possible and the community information can be reserved as much as possible. Experimental results show that our algorithm can not only accurately identify the number of communities of a network, but also obtain higher quality of community partitioning without previously known parameters.

Evolutionary method for finding communities in bipartite networks

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. Here, we show that the finding of communities in such networks can be unified in a general framework-detection of community structure in bipartite networks. Moreover, we propose an evolutionary method for efficiently identifying communities in bipartite networks. To this end, 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 bipartite modularity, we develop a modified adaptive genetic algorithm (MAGA), which is shown to be especially efficient for community structure detection. The high efficiency of the MAGA is based on the following three improvements we make. First, we introduce a different measure for the informativeness of a locus instead of the standard deviation, which can exactly determine which loci mutate. This measure is the bias between the distribution of a locus over the current population and the uniform distribution of the locus, i.e., the Kullback-Leibler divergence between them. Second, we develop a reassignment technique for differentiating the informative state a locus has attained from the random state in the initial phase. Third, we present a modified mutation rule which by incorporating related operations can guarantee the convergence of the MAGA to the global optimum and can speed up the convergence process. Experimental results show that the MAGA outperforms existing methods in terms of modularity for both bipartite and unipartite networks.

Information Bottleneck Based Community Detection in Network

This paper proposes a projection method to transform a unipartite network into a bipartite network. As to the obtained bipartite network, it presents an information-bottleneck-based method for community detection under the information-theoretic framework. This method detects the community structure of networks by finding an efficient compression of the network. The efficient compression holds the regularity of the original network as many as possible. Applications on the computer-generated networks and many real-world networks demonstrate that this method is very effective at community detection of networks. As for the community detection of directed networks, existing methods neglect the direction of edges and treat them as undirected networks. The information provided by directionality is lost in this process. Using the projection method proposed in this paper, the direction of edges can be retained and thus the method is more suitable to detect the community structure in directed networks, such as the world-wide-web. And some new knowledge can be found by the method. In addition, the method can be directly applied to the detection of community structure in bipartite networks, which are common in real world.

Clustering coefficient and community structure of bipartite networks

Many real-world networks display natural bipartite structure, where the basic cycle is a square. In this paper, with the similar consideration of standard clustering coefficient in binary networks, a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed. In order to detect community structures in bipartite networks, two different edge clustering coefficients L C 4 and L C 3 of bipartite networks are defined, which are based on squares and triples respectively. With the algorithm of cutting the edge with the least clustering coefficient, communities in artificial and real world networks are identified. The results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks.