Community Detection Problem Research Articles

MuMod: A Micro-Unit Connection Approach for Hybrid-Order Community Detection

In the past few years, higher-order community detection has drawn an increasing amount of attention. Compared with the lower-order approaches that rely on the connectivity pattern of individual nodes and edges, the higher-order approaches discover communities by leveraging the higher-order connectivity pattern via constructing a motif-based hypergraph. Despite success in capturing the building blocks of complex networks, recent study has shown that the higher-order approaches unavoidably suffer from the hypergraph fragmentation issue. Although an edge enhancement strategy has been designed previously to address this issue, adding additional edges may corrupt the original lower-order connectivity pattern. To this end, this paper defines a new problem of community detection, namely hybrid-order community detection, which aims to discover communities by simultaneously leveraging the lower-order connectivity pattern and the higherorder connectivity pattern. For addressing this new problem, a new Micro-unit Modularity (MuMod) approach is designed. The basic idea lies in constructing a micro-unit connection network, where both of the lower-order connectivity pattern and the higher-order connectivity pattern are utilized. And then a new micro-unit modularity model is proposed for generating the micro-unit groups, from which the overlapping community structure of the original network can be derived. Extensive experiments are conducted on five real-world networks. Comparison results with twelve existing approaches confirm the effectiveness of the proposed method.

Active Learning in the Geometric Block Model

The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical community structures compared with the popular stochastic block model. Galhotra et al. recently proposed a motif-counting algorithm for unsupervised community detection in the geometric block model that is proved to be near-optimal. They also characterized the regimes of the model parameters for which the proposed algorithm can achieve exact recovery. In this work, we initiate the study of active learning in the geometric block model. That is, we are interested in the problem of exactly recovering the community structure of random graphs following the geometric block model under arbitrary model parameters, by possibly querying the labels of a limited number of chosen nodes. We propose two active learning algorithms that combine the use of motif-counting with two different label query policies. Our main contribution is to show that sampling the labels of a vanishingly small fraction of nodes (sub-linear in the total number of nodes) is sufficient to achieve exact recovery in the regimes under which the state-of-the-art unsupervised method fails. We validate the superior performance of our algorithms via numerical simulations on both real and synthetic datasets.

Complex network structure extraction based on community relevance

One way to understand the network function and analyze the network structure is to find the communities of the network accurately. Now, there are many works about designing algorithms for community detection. Most community detection algorithms are based on modularity optimization. However, these methods not only have disadvantages in computational complexity, but also have the problem of resolution restriction. Designing a community detection algorithm that is fast and effective remains a challenge in the field. We attempt to solve the community detection problem in a new perspective in this paper, believing that the assumption used to solve the link prediction problem is useful for the problem of community detection. By using the similarity between modules of the network, we propose a new method to extract the community structure in this paper. Our algorithm consists of three steps. First, we initialize a community partition based on the distribution of the node degree; second, we calculate the similarity between different communities, where the similarity is the index to describe the closeness of the different communities. We assume that the much closer the two different communities are, the greater the likelihood of being divided together; finally, merge the pairs of communities which has the highest similarity value as possible as we can and stop when the condition is not satisfied. Because the convergence of our algorithm is very fast in the process of merging, we find that our method has advantages both in the computational complexity and in the accuracy when compared with other six classical algorithms. Moreover, we design a new measure to describe how difficulty the network division is.

A novel community detection method based on whale optimization algorithm with evolutionary population

Community detection is the process of detecting communities in complex networks. Communities are important structures that can help us further study the properties of complex networks. In recent years, swarm intelligence algorithms have been applied to community detection and have achieved remarkable results. However, these existing algorithms have limited search ability and easily fall into the problem of local optima. In this paper, we propose a new community detection approach based on an improved whale optimization algorithm (WOA). The WOA is applied to a discrete symbol space in solving the community detection problem, therefore topology structure-based search strategies, adjustment and mergence policies, and evolutionary population method are designed to improve the efficiency and effectiveness of the method. Then, a whale optimization algorithm with evolutionary population for community detection (EP-WOCD) is proposed. Extensive experiments are conducted to compare the EP-WOCD with other state-of-the-art algorithms on both artificial and real-world social networks. Experimental results show that the EP-WOCD is effective and stable.

CoVeC: Coarse-grained vertex clustering for efficient community detection in sparse complex networks

This paper tackles the problem of community detection in large-scale graphs. In the literature devoted to this topic, an iterative algorithm, called Louvain Method (LM), stands out as an effective and fast solution for this problem. However, the first iterations of the LM are the most costly. To overcome this issue, this paper introduces CoVeC, a Coarse-grained Vertex Clustering for efficient community detection in sparse complex networks. CoVeC pre-processes the original graph in order to forward a graph of reduced size to the LM. The subsequent group formation, including the maximization of group quality, as per the modularity metric, is left to the LM. We evaluate our proposal using real-world and synthetic networks, presenting distinct sizes and sparsity levels. Overall, our experimental results show that CoVeC can be a way faster option than the first iterations of the LM, yet similarly effective. In fact, for sparser graphs, the combo CoVeC+LM outperforms the standalone LM and its variations, attaining a mean processing time reduction of 47% and a mean modularity reduction of only 0.4%.

Solving dynamic overlapping community detection problem by a multiobjective evolutionary algorithm based on decomposition

Abstract Dynamic and overlapping are two common features of community structures for many real world complex networks. Although there are few studies on detecting dynamic overlapping communities, all those studies only consider a single optimization objective. In practice, it is necessary to evaluate the community detection by multiple metrics to reflect different aspects of a community structure and those metrics may conflict with each other. In this paper, we propose a multi-objective approach based on decomposition for the problem of dynamic overlapping community detection, with consideration of three optimization objectives: partition density (D), extended modularity (EQ), and improved mutual information (NMILFK). The dynamic overlapping network can be regarded as a set of network snapshots. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to detect the communities for each snapshot. To improve the search efficiency, the dynamic optimization technique and a dynamic resource allocation strategy are introduced into the approach. Experiments show that our approach can find uniformly distributed Pareto solutions for the problem and outperforms those comparative approaches.

Detecting multiple communities using quantum annealing on the D-Wave system.

A very important problem in combinatorial optimization is the partitioning of a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the “highest quality” possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network using a quantum annealer.

Community Detection of Multi-Layer Attributed Networks via Penalized Alternating Factorization

Communities are often associated with important structural characteristics of a complex network system, therefore detecting communities is considered to be a fundamental problem in network analysis. With the development of data collection technology and platform, more and more sources of network data are acquired, which makes the form of network as well as the related data more complex. To achieve integrative community detection of a multi-layer attributed network that involves multiple network layers together with their attribute data, effectively utilizing the information from the multiple networks and the attributes may greatly enhance the accuracy of community detection. To this end, in this article, we study the integrative community detection problem of a multi-layer attributed network from the perspective of matrix factorization, and propose a penalized alternative factorization (PAF) algorithm to resolve the corresponding optimization problem, followed by the convergence analysis of the PAF algorithm. Results of the numerical study, as well as an empirical analysis, demonstrate the advantages of the PAF algorithm in community discovery accuracy and compatibility with multiple types of network-related data.

Nature-inspired optimization algorithms for community detection in complex networks: a review and future trends

Over the past couple of decades, the research area of network community detection has seen substantial growth in popularity, leading to a wide range of researches in the literature. Nature-inspired optimization algorithms (NIAs) have given a significant contribution to solving the community detection problem by transcending the limitations of other techniques. However, due to the importance of the topic and its prominence in many applications, the information on it is scattered in various journals, conference proceedings, and patents, and lacked a focused-literature that synthesizes them in a single document. This review aims to provide an overview of the NIAs and their role in solving community detection problems. To achieve this goal, a systematic study is performed on NIAs, followed by historical and statistical analysis of the researches involved. This would lead to the identification of future trends, as well as the discovery of related research challenges. This review provides a guide for researchers to identify new areas of research, as well as directing their future interest towards developing more effective frameworks in the context of nature-inspired community detection algorithms.

Block diagonal dominance-based dynamic programming for detecting community

Clustering or partition is a fundamental work for graph or network. Detecting communities is a typical clustering, which divides a network into several parts according to the modularity. Community detection is a critical challenge for designing scalable, adaptive and survivable trust management protocol for a community of interest-based social IoT system. Most of the existed methods on community detection suffer from a common issue that the number of communities should be prior decided. This urges us to estimate the number of communities from the data by some way. This paper concurrently considers eliminating the number of communities and detecting communities based on block diagonal dominace adjacency matrix. To construct a block diagonal dominance adjacency matrix for the input network, it first reorders the node number by the breadth-first search algorithm. For the block diagonal dominance adjacency matrix, this paper shows that the numbers of nodes in a community should be continuous adjacent. And thus, it only needs insert some breakpoints in node number sequence to decide the number of communities and the nodes in every community. In addition, a dynamic programming algorithm is designed to achieve an optimal community detection result. Experimental results on a number of real-world networks show the effectiveness of the dynamic programming approach on the community detection problem.

Towards effective discovery of natural communities in complex networks and implications in e-commerce

Automated community detection is an important problem in the study of complex networks. The idea of community detection is closely related to the concept of data clustering in pattern recognition. Data clustering refers to the task of grouping similar objects and segregating dissimilar objects. The community detection problem can be thought of as finding groups of densely interconnected nodes with few connections to nodes outside the group. A node similarity measure is proposed here that finds the similarity between two nodes by considering both neighbors and non-neighbors of these two nodes. Subsequently, a method is introduced for identifying communities in complex networks using this node similarity measure and the notion of data clustering. The significant characteristic of the proposed method is that it does not need any prior knowledge about the actual communities of a network. Extensive experiments on several real world and artificial networks with known ground-truth communities are reported. The proposed method is compared with various state of the art community detection algorithms by using several criteria, viz. normalized mutual information, f-measure etc. Moreover, it has been successfully applied in improving the effectiveness of a recommender system which is rapidly becoming a crucial tool in e-commerce applications. The empirical results suggest that the proposed technique has the potential to improve the performance of a recommender system and hence it may be useful for other e-commerce applications.

Exact Blind Community Detection From Signals on Multiple Graphs

Networks and data supported on graphs have become ubiquitous in the sciences and engineering. This paper studies the 'blind' community detection problem, where we seek to infer the community structure of a graph model given the observation of independent graph signals on a set of nodes whose connections are unknown. We model each observation as filtered white noise, where the underlying network structure varies with every observation. These varying network structures are modeled as independent realizations of a latent planted partition model (PPM), justifying our assumption of a constant underlying community structure over all observations. Under certain conditions on the graph filter and PPM parameters, we propose algorithms for determining (i) the number of latent communities and (ii) the associated partitions of the PPM. We then prove statistical guarantees in the asymptotic and non-asymptotic sampling cases. Numerical experiments on real and synthetic data demonstrate the efficacy of our algorithms.

Fuzzy Measures: A solution to deal with community detection problems for networks with additional information

In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.

A Temporal User Attribute-Based Algorithm to Detect Communities in Online Social Networks

The world is witnessing the daily emergence of a vast variety of online social networks and community detection problem is a major research area in online social network studies. The existing community detection algorithms are mostly edge-based and are evaluated using the modularity metric benchmarks. However, these algorithms have two inherent limitations. Firstly, they are based on a pure mathematical object which considers the number of connections in each community as the main measures. Consequently, a resolution limit and low accuracy in finding community members in often observed. Whereas, online social networks are dynamic networks and the key players are humans whose main attributes such as lifespan, geo-location, the density of interactions, and user weight, change over time. These attributes tend to influence the formation of user communities in any category of online social network. Secondly, the output structure of existing community detection algorithms is usually provided as a graph and dendrogram. A graph structure, is, however, characterized by a high memory complexity, and subsequently exponential search time complexity. Implementing dendrogram such a complex structure is complicated. To address memory complexity and the accuracy rate of the community detection issues, this paper proposes a new temporal user attribute-based algorithm, namely the recently largest interaction based on the attributes of a typical online social network user. Experimental results show that the proposed algorithm outperforms eight well-known algorithms in this domain.

Clustering Social Networks using Nature-inspired BAT Algorithm

The widespread extent of internet availability at low cost impels user activities on social media. As a result, a huge number of networks with a lot of varieties are easily accessible. Community detection is one of the significant tasks to understand the behavior and functionality of such real-world networks. Mathematically, community detection problem has been modeled as an optimization problem and various meta-heuristic approaches have been applied to solve the same. Progressively, many new nature-inspired algorithms have also been explored to handle the diverse optimization problems in the last decade. In this paper, nature-inspired Bat Algorithm (BA) is adopted and a new variant of Discrete Bat algorithm (NVDBA) is recommended to identify the communities from social networks. The recommended scheme does not require the number of communities as a prerequisite. The experiments on a number of real-world networks have been performed to assess the performance of the proposed approach which in turn confirms its validity. The results confirm that the recommended algorithm is competitive with other existing methods and offers promising results for identifying communities in social networks.

A variant of EAM to uncover community structure in complex networks

Environmental adaptation method (EAM) was developed to solve single-objective optimisation problems. After the first proposal, other variants have been suggested to speed up the convergence rate and to maintain the diversity of the solutions. Among those variants, IEAM-RP works with real numbers. In this paper, a variant of IEAM-RP has been suggested with major changes in adaptation operator to improve the overall performance of the algorithm. In the proposed method, significant attention has been given for balancing exploration and exploitation of individuals in the population. The performance of the proposed algorithm is compared against 14 state-of-the-art algorithms using standard benchmark functions of the comparing continuous optimisers (COCO) framework. Further, to check the effectiveness of the proposed approach, it has been applied to a real-world problem of community detection in complex networks. Again, the experimental results are found very promising and competitive compared to other algorithms.

A Memetic Algorithm for Community Detection in Signed Networks

Community discovery (i.e. community detection) in signed networks is a division of nodes, such that the edges in the communities are positive and the edges between the communities are negative. Davis and Harary have solved the problem of community detection when a signed graph is balanced or weakly balanced. When the signed network is unbalanced, community detection becomes very complex. In this paper, we propose a novel memetic algorithm (MA) called MACD-SN for community partition (i.e. community detection) in signed networks. Firstly, we present a novel initialization algorithm used in initialization of MACD-SN. This method can accelerate the convergence rate of MACD-SN algorithm. Next, in addition to using frequently-used variation operation (in this paper, variation and mutation are interchangeable), this paper presents a novel crossover operation and a novel variation operation, which contributes to increasing the correctness of the MACD-SN algorithm's operation result and reduces its running time. Lastly, this paper proposes a new local search algorithm, which may enable the algorithm's result to jump away the local best result with a certain probability and draw near the global best result quickly. For testing the performance of MACD-SN algorithm, we have done many experiments using five kinds of synthetic signed networks and five real-world signed networks. The test outcomes show that the proposed algorithm is valid and efficient for signed network cluster partition (i.e. community detection).

Known by Who We Follow: A Biclustering Application to Community Detection

The detection of communities in social networks is a task with multiple applications both in research and in sectors such as marketing and politics among others. In this paper, we address the task of detecting on-line communities of Twitter users for a given domain. Our main contribution consists in modelling the community detection problem as a biclustering task. We have performed the experimentation with data from the political domain, a very dynamic area with a large number of interested users and a high availability of tweets. We have evaluated our proposal using both extrinsic and intrinsic methods, reaching very good results in both cases. We use the silhouette coefficient as intrinsic metric for clustering evaluation, and a classification task of political leanings of Twitter users as extrinsic evaluation. One of the most interesting conclusions of our experiments is the quality, from the point of view of predictive capacity in the classification task, of the communities identified with the proposed method. The information provided by communities detected through “follow” relationships has a predictive capacity comparable to that of the contents of tweets written by users. The results also show how detected communities can give insights about future events related to these communities that arise around social networks.

Community detection in complex networks using multi-objective bat algorithm

Community detection is the problem of identifying communities in which we aim to discover groups of nodes with high connectivity within the same group and with low connectivity outside the group. Community detection is considered to be a non-deterministic polynomial-time hard problem. Heuristic algorithms can be used to solve such a complex optimisation problem. Bat algorithm (BA) is a meta-heuristic optimisation algorithm. The BA can be used to model a multi-objective optimisation problem. In this paper, the multi-objective bat algorithm (MOBA) is adapted to model and solve the community detection problem. In order to evaluate the algorithm, four real-world datasets are used. The performance of the algorithm is compared with seven other methods from the literature. The comparison was in terms of two metrics to check the quality of the obtained community namely modularity (Q) and normalised mutual information (NMI). The results show that the proposed algorithm outperforms all algorithms in one dataset and that it is competitive in other cases.

Identification of complex network topologies through delayed mutual information

The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its associated local dynamics. Delayed mutual information is also used to solve the community detection problem. A probabilistic voter model defined on a scale-free graph is used throughout the paper as an illustrative example.