Communities In Bipartite Networks Research Articles

Community detection in bipartite networks with stochastic block models.

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 bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of sqrt[2], and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

Modularity and projection of bipartite networks

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 different modularity function and sees different aspects of the bipartite structure. Based on these results we suggest a simple ‘rule of thumb’ for finding communities in bipartite networks.

A Bayesian Inference Method Using Monte Carlo Sampling for Estimating the Number of Communities in Bipartite Networks

Community detection is an important analysis task for complex networks, including bipartite networks, which consist of nodes of two types and edges connecting only nodes of different types. Many community detection methods take the number of communities in the networks as a fixed known quantity; however, it is impossible to give such information in advance in real-world networks. In our paper, we propose a projection-free Bayesian inference method to determine the number of pure-type communities in bipartite networks. This paper makes the following contributions: (1) we present the first principle derivation of a practical method, using the degree-corrected bipartite stochastic block model that is able to deal with networks with broad degree distributions, for estimating the number of pure-type communities of bipartite networks; (2) a prior probability distribution is proposed over the partition of a bipartite network; (3) we design a Monte Carlo algorithm incorporated with our proposed method and prior probability distribution. We give a demonstration of our algorithm on synthetic bipartite networks including an easy case with a homogeneous degree distribution and a difficult case with a heterogeneous degree distribution. The results show that the algorithm gives the correct number of communities of synthetic networks in most cases and outperforms the projection method especially in the networks with heterogeneous degree distributions.

Finding maximal bicliques in bipartite networks using node similarity

In real world complex networks, communities are usually both overlapping and hierarchical. A very important class of complex networks is the bipartite networks. Maximal bicliques are the strongest possible structural communities within them.Here we consider overlapping communities in bipartite networks and propose a method that detects an order-limited number of overlapping maximal bicliques covering the network. We formalise a measure of relative community strength by which communities can be categorised, compared and ranked. There are very few real bipartite datasets for which any external ground truth about overlapping communities is known. Here we test three such datasets. We categorise and rank the maximal biclique communities found by our algorithm according to our measure of strength. Deeper analysis of these bicliques shows they accord with ground truth and give useful additional insight. Based on this we suggest our algorithm can find true communities at the first level of a hierarchy. We add a heuristic merging stage to the maximal biclique algorithm to produce a second level hierarchy with fewer communities and obtain positive results when compared with other overlapping community detection algorithms for bipartite networks.

A Memetic Algorithm for Community Detection in Bipartite Networks

Bipartite networks belong to the category of complex networks, whose vertices can be divided into two separated vertex sets, so that there are no edges between vertices in the same set, and edges only exist between vertices in different sets. In the past decades, although community discovery in one-mode networks has been deeply explored, the detection of communities in bipartite networks has not been widely studied. In this paper, we present a new memetic algorithm named MATMCD-BN for community detection in bipartite networks with two types of nodes in the community. Firstly, we put forward a new initialization method for population initialization of memetic algorithm for bipartite network communities discovery, which can expedite the convergence speed of this algorithm. Secondly, besides using traditional mutation operator, we propose a new crossover operator (called two-way random crossover operator in this paper) and a new mutation operator (called mutation operator 2 in this paper), which are helpful to improve the accuracy of the solution and accelerate the convergence speed of the proposed algorithm. Finally, we develop a local search method, which can make the solution approach the global optimal solution quickly and jump out of the local optimal solution with a certain probability. As far as we know, the proposed MATMCD-BN is the first memetic algorithm (MA) applied to community detection in bipartite networks with two types of nodes in the community. In order to confirm the performance of this algorithm, we have done a lot of experiments using synthetic and real social networks. The experimental results demonstrate that the presented method is effective and promising for bipartite network community identification.

A spectral method to find communities in bipartite networks

Community detection in complex networks that aims to find partitions of networks with dense intra-edges and sparse inter-edges, has recently attracted lots of interest in many fields. Specially, bipartite networks composed of two different types of vertices are the common representations for many real-world networks, such as actor–film, consumer–product networks, etc. In this paper, we show that optimizing Barber’s bipartite modularity, which is widely used to evaluate partitions of bipartite networks, can be reformulated as a spectral problem with appropriate relaxations. We further propose a new method combining singular value decomposition(SVD) and BRIM algorithm to obtain an optimal community partition. Compared with many other algorithms, the new method can give us a more detailed and comprehensive view of the original bipartite network for different cluster numbers k. We test our method on both synthetic networks and two benchmark data sets. Experimental results show that, our method is not only capable to extract a community partition with a larger bipartite modularity, but also converge to the exact underlying community partition when k is appropriately set, which helps to alleviate the resolution limit issue to some extent.

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.

Efficient Detection of Communities in Biological Bipartite Networks.

Methods to efficiently uncover and extract community structures are required in a number of biological applications where networked data and their interactions can be modeled as graphs, and observing tightly-knit groups of vertices ("communities") can offer insights into the structural and functional building blocks of the underlying network. Classical applications of community detection have largely focused on unipartite networks - i.e., graphs built out of a single type of objects. However, due to increased availability of biological data from various sources, there is now an increasing need for handling heterogeneous networks which are built out of multiple types of objects. In this paper, we address the problem of identifying communities from biological bipartite networks - i.e., networks where interactions are observed between two different types of objects (e.g., genes and diseases, drugs and protein complexes, plants and pollinators, and hosts and pathogens). Toward detecting communities in such bipartite networks, we make the following contributions: i) (metric) we propose a variant of bipartite modularity; ii) (algorithms) we present an efficient algorithm called biLouvain that implements a set of heuristics toward fast and precise community detection in bipartite networks (https://github.com/paolapesantez/biLouvain); and iii) (experiments) we present a thorough experimental evaluation of our algorithm including comparison to other state-of-the-art methods to identify communities in bipartite networks. Experimental results show that our biLouvain algorithm identifies communities that have a comparable or better quality (as measured by bipartite modularity) than existing methods, while significantly reducing the time-to-solution between one and four orders of magnitude.

Core of communities in bipartite networks.

We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the coauthorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and the adjusted Wallace index, respectively. The detection of cores is highly precise, although the accuracy of the methodology can be limited in some cases.

Improving the recommender algorithms with the detected communities in bipartite networks

Recommender system offers a powerful tool to make information overload problem well solved and thus gains wide concerns of scholars and engineers. A key challenge is how to make recommendations more accurate and personalized. We notice that community structures widely exist in many real networks, which could significantly affect the recommendation results. By incorporating the information of detected communities in the recommendation algorithms, an improved recommendation approach for the networks with communities is proposed. The approach is examined in both artificial and real networks, the results show that the improvement on accuracy and diversity can be 20% and 7%, respectively. This reveals that it is beneficial to classify the nodes based on the inherent properties in recommender systems.

Quantitative function and algorithm for community detection in bipartite networks

Community detection in complex networks is a topic of high interest in many scientific fields. A bipartite network is a special type of complex network whose nodes are decomposed into two disjoint sets such that no two nodes within the same set are adjacent. Many relationships in real-world systems can be represented by a bipartite network, such as predator-prey relationships, plant-pollinator interactions, and drug-target interactions. 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 early stage. Several quantitative functions have been developed for evaluating the quality of bipartite network divisions, however, these functions were designed based on null model comparisons and thus are subject to certain resolution limits. In this paper, we propose a new quantitative function called bipartite partition density for community detection in bipartite networks, and use some network examples to demonstrate that this quantitative function is superior to the widely used Barber’s bipartite modularity and other functions. Based on the bipartite partition density, the bipartite network community detection problem is formulated into an integer nonlinear programming model in which a bipartite network can be partitioned into reasonable overlapping communities by maximizing the quantitative function. We further develop a heuristic adapted label propagation algorithm (BiLPA) to optimize the bipartite partition density in large-scale bipartite networks. BiLPA is efficient and does not require any prior knowledge about the number of communities in the networks. We conduct extensive experiments on simulated and real-world networks and demonstrate that BiLPA can successfully identify the community structures of bipartite networks.

Asymmetric intimacy and algorithm for detecting communities in bipartite networks

Abstract In this paper, an algorithm to choose a good partition in bipartite networks has been proposed. Bipartite networks have more theoretical significance and broader prospect of application. In view of distinctive structure of bipartite networks, in our method, two parameters are defined to show the relationships between the same type nodes and heterogeneous nodes respectively. Moreover, our algorithm employs a new method of finding and expanding the core communities in bipartite networks. Two kinds of nodes are handled separately and merged, and then the sub-communities are obtained. After that, objective communities will be found according to the merging rule. The proposed algorithm has been simulated in real-world networks and artificial networks, and the result verifies the accuracy and reliability of the parameters on intimacy for our algorithm. Eventually, comparisons with similar algorithms depict that the proposed algorithm has better performance.

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.

Community detection in bipartite networks using weighted symmetric binary matrix factorization

In this paper, we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describes the 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.

An MDL approach to efficiently discover communities in bipartite network

An minimum description length (MDL) criterion is proposed to choose a good partition for a bipartite network. A heuristic algorithm based on combination theory is presented to approach the optimal partition. As the heuristic algorithm automatically searches for the number of partitions, no user intervention is required. Finally, experiments are conducted on various datasets, and the results show that our method generates higher quality results than the state-of-art methods, cross-association and bipartite, recursively induced modules. Experiment results also show the good scalability of the proposed algorithm. The method is applied to traditional Chinese medicine (TCM) formula and Chinese herbal network whose community structure is not well known, and found that it detects significant and it is informative community division.

Dual modularity optimization for detecting overlapping communities in bipartite networks

Many algorithms have been designed to discover community structure in networks. These algorithms are mostly dedicated to detecting disjoint communities. Very few of them are intended to discover ov...

Comment on “Evolutionary method for finding communities in bipartite networks”

In a recent paper, Zhan, Zhang, Guan, and Zhou [Phys. Rev. E 83, 066120 (2011)] presented a modified adaptive genetic algorithm (MAGA) tailored to the discovery of maximum modularity partitions of the node set into communities in unipartite, bipartite, and directed networks. The authors claim that "detection of communities in unipartite networks or in directed networks can be transformed into the same task in bipartite networks." Actually, some tests show that it is not the case for the proposed transformations, and why. Experimental results of MAGA for modularity maximization of untransformed unipartite or bipartite networks are also discussed.

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.

Biclique communities

We present a method for detecting communities in bipartite networks. Based on an extension of the k -clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping bicliques. If bipartite information is available, the biclique community detection algorithm retains all of the advantages of the k -clique algorithm, but avoids discarding important structural information when performing a one-mode projection of the network. Further, the biclique community detection algorithm provides a level of flexibility by incorporating independent clique thresholds for each of the nonoverlapping node sets in the bipartite network.