Community Detection In Multilayer Networks Research Articles

A weighted prior tensor train decomposition method for community detection in multi-layer networks

Community detection in multi-layer networks stands as a prominent subject within network analysis research. However, the majority of existing techniques for identifying communities encounter two primary constraints: they lack suitability for high-dimensional data within multi-layer networks and fail to fully leverage additional auxiliary information among communities to enhance detection accuracy. To address these limitations, a novel approach named weighted prior tensor training decomposition (WPTTD) is proposed for multi-layer network community detection. Specifically, the WPTTD method harnesses the tensor feature optimization techniques to effectively manage high-dimensional data in multi-layer networks. Additionally, it employs a weighted flattened network to construct prior information for each dimension of the multi-layer network, thereby continuously exploring inter-community connections. To preserve the cohesive structure of communities and to harness comprehensive information within the multi-layer network for more effective community detection, the common community manifold learning (CCML) is integrated into the WPTTD framework for enhancing the performance. Experimental evaluations conducted on both artificial and real-world networks have verified that this algorithm outperforms several mainstream multi-layer network community detection algorithms.

Motif-based community detection in heterogeneous multilayer networks

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

Consistent community detection in inter-layer dependent multi-layer networks

Community detection in multi-layer networks, which aims at finding groups of nodes with similar connective patterns among all layers, has attracted tremendous interests in multi-layer network analysis. Most existing methods are extended from those for single-layer networks, which assume that different layers are independent. In this paper, we propose a novel community detection method in multi-layer networks with inter-layer dependence, which integrates the stochastic block model (SBM) and the Ising model. The community structure is modeled by the SBM model and the inter-layer dependence is incorporated via the Ising model. An efficient alternative updating algorithm is developed to tackle the resultant optimization task. Moreover, the asymptotic consistencies of the proposed method in terms of both parameter estimation and community detection are established, which are supported by extensive simulated examples and a real example on a multi-layer malaria parasite gene network.

Evaluating Community Detection Algorithms for Multilayer Networks: Effectiveness of Link Weights and Link Direction

Analyzing the structures of multilayer networks (MLNs) has been a hot research topic in network science. Community detection algorithms are important tools for analyzing MLNs. In the literature, several community detection algorithms for MLNs have been proposed. Moreover, there are several options for the graph representation of an MLN: for example, directed or undirected, weighted or unweighted, and using information from all or only some layers. Although these options may affect the results of community detection in MLNs, representations that are effective for community detection have not yet been clarified. In this paper, we experimentally evaluate the effectiveness of three types of community detection algorithms for MLNs and examine how the graph representation of an MLN affects the results of these algorithms. Our main findings are as follows: (1) The flattening approach is particularly effective, whereas the layer-by-layer approach is not applicable to detecting communities in MLNs of Twitter users. (2) Using a directed graph for each layer of an MLN increases the accuracy of community detection. (3) The Leiden method, which is a community detection algorithm for single-layer networks, achieves comparable accuracy with the community detection algorithms for MLNs, which suggests that there exists room for improvement in multilayer community detection algorithms for effectively utilizing the multilayer structures of MLNs.

Efficient community detection in multilayer networks using boolean compositions.

Networks (or graphs) are used to model the dyadic relations between entities in complex systems. Analyzing the properties of the networks reveal important characteristics of the underlying system. However, in many disciplines, including social sciences, bioinformatics, and technological systems, multiple relations exist between entities. In such cases, a simple graph is not sufficient to model these multiple relations, and a multilayer network is a more appropriate model. In this paper, we explore community detection in multilayer networks. Specifically, we propose a novel network decoupling strategy for efficiently combining the communities in the different layers using the Boolean primitives AND, OR, and NOT. Our proposed method, network decoupling, is based on analyzing the communities in each network layer individually and then aggregating the analysis results. We (i) describe our network decoupling algorithms for finding communities, (ii) present how network decoupling can be used to express different types of communities in multilayer networks, and (iii) demonstrate the effectiveness of using network decoupling for detecting communities in real-world and synthetic data sets. Compared to other algorithms for detecting communities in multilayer networks, our proposed network decoupling method requires significantly lower computation time while producing results of high accuracy. Based on these results, we anticipate that our proposed network decoupling technique will enable a more detailed analysis of multilayer networks in an efficient manner.

A study on community detection in multilayer networks

Studying complex networks is essential for a better understanding of network science. Many studies have been done on single-layer networks in complex networks. After the advancement and widespread usage of the internet and social media networks, performing community detection in multilayer networks becomes essential to reach more people and work with different personalities on different platforms. Motivated by this observation, this paper has studied types of networks, metrics, measures, and community detection using deep learning-based models in multilayer networks. This survey can play a significant role in analyzing and understanding multilayer networks.

A stochastic block Ising model for multi-layer networks with inter-layer dependence.

Community detection has attracted tremendous interests in network analysis, which aims at finding group of nodes with similar characteristics. Various detection methods have been developed to detect homogeneous communities in multi-layer networks, where inter-layer dependence is a widely acknowledged but severely under-investigated issue. In this paper, we propose a novel stochastic block Ising model (SBIM) to incorporate the inter-layer dependence to help with community detection in multi-layer networks. The community structure is modeled by the stochastic block model (SBM) and the inter-layer dependence is incorporated via the popular Ising model. Furthermore, we develop an efficient variational EM algorithm to tackle the resultant optimization task and establish the asymptotic consistency of the proposed method. Extensive simulated examples and a real example on gene co-expression multi-layer network data are also provided to demonstrate the advantage of the proposedmethod.

Community Detection in Multilayer Networks Via Semi-Supervised Joint Symmetric Nonnegative Matrix Factorization

Community detection plays an important role in network analysis and has attracted considerable interest from researchers. In the past few decades, various community detection algorithms have been developed for single networks. However, in the real world, relationships between nodes are often of multiple natures, such as friendship, kinship and common interests among people in social networks. These relationships can be modeled by a multilayer network. Thus, identifying communities in multilayer networks has become a challenging problem. The existing algorithms for multilayer networks only utilize the topological structure and ignore the prior information, thereby resulting in low accuracy. In this paper, by combining the graph regularization with the prior information, we propose a semi-supervised joint symmetric nonnegative matrix factorization(SSJSNMF) algorithm for community detection in multilayer networks. We use graph regularization term to penalize the latent space dissimilarity of some nodes when prior information shows that these nodes belong to same community. Then, by fusing graph regularization into a joint symmetric nonnegative matrix factorization(NMF) model, the proposed model can utilize the topological structure information and prior information simultaneously. Furthermore, we develop effective multiplicative updating rules to solve the proposed model. Finally, numerical experiments demonstrate that SSSNMF outperforms some existing algorithms.

Community Detection in Multilayer Networks Based on Matrix Factorization and Spectral Embedding Method

Community detection remains a challenging research hotspot in network analysis. With the complexity of the network data structures increasing, multilayer networks, in which entities interact through multiple types of connections, prove to be effective in describing complex networks. The layers in a multilayer network may not share a common community structure. In this paper, we propose a joint method based on matrix factorization and spectral embedding to recover the groups not only for the layers but also for nodes. Specifically, the layers are grouped via the matrix factorization method with layer similarity-based regularization in the perspective of a mixture multilayer stochastic block model, and then the node communities within a layer group are revealed by clustering a combination of the spectral embedding derived from the adjacency matrices and the shared approximation matrix. Numerical studies show that the proposed method achieves competitive clustering results as the number of nodes and/or number of layers vary, together with different topologies of network layers. Additionally, we apply the proposed method on two real-world multilayer networks and obtain interesting findings which again highlight the effectiveness of our method.

Covariate-Assisted Community Detection in Multi-Layer Networks

ABSTRACT Communities in multi-layer networks consist of nodes with similar connectivity patterns across all layers. This article proposes a tensor-based community detection method in multi-layer networks, which leverages available node-wise covariates to improve community detection accuracy. This is motivated by the network homophily principle, which suggests that nodes with similar covariates tend to reside in the same community. To take advantage of the node-wise covariates, the proposed method augments the multi-layer network with an additional layer constructed from the node similarity matrix with proper scaling, and conducts a Tucker decomposition of the augmented multi-layer network, yielding the spectral embedding vector of each node for community detection. Asymptotic consistencies of the proposed method in terms of community detection are established, which are also supported by numerical experiments on various synthetic networks and two real-life multi-layer networks.

Multilayer cellular learning automata: A computational model to solve multilayer infrastructure problems with its application in community detection for multilayer networks

Multilayer networks are one type of complex systems that have multiple types of interactions among their nodes. Through the development and extension of the real-world networks, especially social and biological networks, understanding the structure and organization of multilayer systems become more significant. In this paper, we propose a new computational model based on learning automata to overcome the problems related to multilayer networks. In our proposed model, the whole network is modeled as a set of layers in which an irregular cellular learning automata (ICLA) is assigned to each node in a layer. The functionality of cellular learning automata (CLA) is dependent on two important features: local and global environments. In this model, the information from the other layers is evaluated as the global environments, and update rules are performed based on the information from the other layers. Finally, by the convergence of CLA in each layer the global environments cause the multilayer cellular learning automata (MLCLA) to cover all possible states in all nodes of layers. We apply this model to community detection in multilayer networks as an example of the application of the proposed model. To solve this, each CLA by the depth-first search algorithm detects the optimal community in a layer and then sends the information about the identified community to the next layer as a feature vector. The simulation results on multiple well-known multilayer datasets demonstrate the effectiveness and superiority of the proposed algorithm in terms of similarity and modularity measures, and the analysis results of the proposed algorithm in terms of Precision, Recall, and F1-score are higher than the other available community detection methods.

Community detection for multilayer weighted networks

Multilayer networks are used to encode multiple types of relations arising in complex systems and have received significant attention in recent years. Community detection in multilayer networks is an important issue in various fields; hence, stochastic block models have emerged as a popular probabilistic framework over the past decades. However, stochastic block models are suited to binary networks rather than weighted networks. A generalised stochastic block model is proposed herein to address multilayer sparse or dense weighted networks. A variational expectation-maximisation algorithm is derived to estimate the parameters of interest. In addition, an upper bound is derived for the probability of misclassification, which is governed by the Rényi divergence of order 12. Furthermore, our model is compared with four competing methods on synthetic networks. Finally, our approach is examined on financial markets and bicycle sharing systems.

Community detection on mixture multilayer networks via regularized tensor decomposition

We study the problem of community detection in multilayer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, that is, mixture multilayer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multilayer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.

Null Models and Community Detection in Multi-Layer Networks

Multi-layer networks of multiplex type represent relational data on a set of entities (nodes) with multiple types of relations (edges) among them where each type of relation is represented as a network layer. A large group of popular community detection methods in networks are based on optimizing a quality function known as the modularity score, which is a measure of the extent of presence of module or community structure in networks compared to a suitable null model. Here we introduce several multi-layer network modularity and model likelihood quality function measures using different null models of the multi-layer network, motivated by empirical observations in networks from a diverse field of applications. In particular, we define multi-layer variants of the Chung-Lu expected degree model as null models that differ in their modeling of the multi-layer degrees. We propose simple estimators for the models and prove their consistency properties. A hypothesis testing procedure is also proposed for selecting an appropriate null model for data. These null models are used to define modularity measures as well as model likelihood based quality functions. The proposed measures are then optimized to detect the optimal community assignment of nodes (Code available at: https://u.osu.edu/subhadeep/codes/ ). We compare the effectiveness of the measures in community detection in simulated networks and then apply them to four real multi-layer networks.

Multi-objective optimization for community detection in multilayer networks

Community detection in multilayer networks plays a key role in revealing the multiple aspects of information spreading and in comprehending the relationships and interactions within and between each layer. However, most existing algorithms are prone to local optimality, and they are also difficult to extend to high-dimensional networks. To address these challenges, we propose here a multi-objective algorithm for community detection that is based on the genetic algorithm. In particular, the modularity is introduced to optimize each network layer iteratively, and the local search is combined with genetic operations to overcome local optimality. Comparative benchmarks with other algorithms on artificial and real-world networks show that the proposed algorithm performs better, especially on high-dimensional networks.

Leveraging semantic for community mining in multilayer networks

Community detection in multilayer networks aims to identify groups of well-connected nodes across multiple layers. While existing methods have been developed to deal with large graphs with few layers (typically less than 10), many real-world datasets are structured by transitive relationships that give rise to networks with thousands of extremely dense layers (e.g. co-citation networks, IMDb actor graphs, co-reference information network, social net- works). In addition, in these datasets the layers are often associated with textual summaries which provide important and hitherto unexploited information on the nature of the relation encoded by the layer. In this paper, we propose a new method which exploits the text associated with the layers in order to identify communities grouping together nodes connected through several semantically close layers. The method consists in embedding layer textual information in an Euclidean space, and to use it to group together, in the same community, nodes belonging to semantically close layers. To that end, we develop a pattern mining approach that extracts communities from numerical data. This approach, which mixes both symbolic and numeric techniques, is particularly well suited to identify communities in multilayer graphs. Indeed, we show that it obtains more diverse and better quality communities than those obtained by state-of-the-art competitors on datasets where ground truth is known. We also show that taking into account the semantic information improves the quality of the communities.

Identification of multi-layer networks community by fusing nonnegative matrix factorization and topological structural information

The accumulated multi-layer networks in nature and society provide a great opportunity for revealing the mechanisms of the underlying complex systems with multiple types of interactions. Community detection in multi-layer networks aims to extract well-connected groups of vertices for all layers, which shed light into revealing the structure–function relations. The current algorithms either exploit the topological structure of multi-layer networks or explore the latent features of networks, which are criticized due to their low accuracy because they ignore the relation among various layers. To attack these problems, a novel algorithm for Multi-layer community detection by using joint Nonnegative Matrix Factorization (MjNMF) is proposed, which simultaneously considers the topological structure and relations of layers. Specifically, MjNMF extracts features of vertices for each layer by simultaneously factorizing the adjacency matrices of all layers with a common basis matrix, where features of vertices preserve the topological structure of all layers. To obtain community structure, MjNMF decomposes the similarity matrices of vertices for all layers in concern. The smoothness strategy is adopted to connect features of various layers with community structure by learning a project matrix for each layer. Finally, MjNMF integrates feature extraction, community detection, and smoothness by formulating an overall objective function, and derives the optimization rules. The experimental results on ten multi-layer networks demonstrate the proposed algorithm significantly outperforms thirteen state-of-the-art methods in terms of various measurements.

Modularity in Multilayer Networks Using Redundancy-Based Resolution and Projection-Based Inter-Layer Coupling

The generalized version of modularity for multilayer networks, a.k.a. multislice modularity, is characterized by two model parameters, namely resolution factor and inter-layer coupling factor. The former corresponds to a notion of layer-specific relevance, whereas the inter-layer coupling factor represents the strength of node connections across the network layers. Despite the potential of this approach, the setting of both parameters can be arbitrarily selected, without considering specific characteristics from the topology of the multilayer network as well as from an available community structure. Also, the multislice modularity is not designed to explicitly model order relations over the layers, which is of prior importance for dynamic networks. This paper aims to overcome the main limitations of the multislice modularity by introducing a new formulation of modularity for multilayer networks. We revise the role and semantics of both the resolution and inter-layer coupling factors based on information available from the within-layer and inter-layer structures of the multilayer communities. Also, our proposed multilayer modularity is general enough to consider orderings of network layers and their constraints on layer coupling. Experiments were carried out on synthetic and real-world multilayer networks using state-of-the-art approaches for multilayer community detection. The obtained results have shown the meaningfulness of the proposed modularity, revealing the effects of different combinations of the resolution and inter-layer coupling functions. This work also represents a starting point for the development of new optimization methods for community detection in multilayer networks.

Spectral and matrix factorization methods for consistent community detection in multi-layer networks

We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these “intermediate fusion” methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain largely unexplored. In the absence of statistical guarantees on the objective functions, it is difficult to determine if the algorithms optimizing the objectives will return good community structures. We investigate the consistency properties of the global optimizer of some of these objective functions under the multi-layer stochastic blockmodel. For this purpose, we derive several new asymptotic results showing consistency of the intermediate fusion techniques along with the spectral clustering of mean adjacency matrix under a high dimensional setup, where the number of nodes, the number of layers and the number of communities of the multi-layer graph grow. Our numerical study shows that the intermediate fusion techniques outperform late fusion methods, namely spectral clustering on aggregate spectral kernel and module allegiance matrix in sparse networks, while they outperform the spectral clustering of mean adjacency matrix in multi-layer networks that contain layers with both homophilic and heterophilic communities.

Multi-layer network community detection model based on attributes and social interaction intensity

With the rapid development of mobile communications and electronic technology, relevant network systems have become larger in scale and exhibited different hierarchical relationships. The complex relationships and links among different users make it more difficult to ultimately obtain data on a whole system. Even with the availability of powerful aggregation tools, most companies cannot afford the associated human and financial costs. However, existing multi-layer network community detection methods are well suited for attribute-based community detection. Therefore, this paper proposes a multi-layer local community detection model that is based on attribute and structure information. This model can effectively utilize node attribute information and the similarity strength information revealed by social exchanges to improve the accuracy of community detection in multi-layer networks. Unlike classical multi-layer and global community detection algorithms, this algorithm is robust on most datasets because of its modularity and computational efficiency.