Temporal Community Detection and Analysis with Network Embeddings

Network embedding, aiming to learn the low-dimensional representations of nodes in networks, is of paramount importance in many real applications. One basic requirement of network embedding is to preserve the structure and inherent properties of the networks. While previous network embedding methods primarily preserve the microscopic structure, such as the first- and second-order proximities of nodes, the mesoscopic community structure, which is one of the most prominent feature of networks, is largely ignored. In this paper, we propose a novel Modularized Nonnegative Matrix Factorization (M-NMF) model to incorporate the community structure into network embedding. We exploit the consensus relationship between the representations of nodes and community structure, and then jointly optimize NMF based representation learning model and modularity based community detection model in a unified framework, which enables the learned representations of nodes to preserve both of the microscopic and community structures. We also provide efficient updating rules to infer the parameters of our model, together with the correctness and convergence guarantees. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over the state-of-the-arts.

Network embedding (graph embedding) has become the focus of studying graph structure in recent years. In addition to the research on homogeneous networks and heterogeneous networks, there are also some methods to attempt to solve the problem of dynamic network embedding. However, in dynamic networks, there is no research method specifically for heterogeneous networks. Therefore, this paper proposes a heterogeneous dynamic graph attention network (HDGAN), which attempts to use the attention mechanism to take the heterogeneity and dynamics of the network into account at the same time, so as to better learn network embedding. Our method is based on three levels of attention, namely structural-level attention, semantic-level attention and time-level attention. Structural-level attention pays attention to the network structure itself, and obtains the representation of structural-level nodes by learning the attention coefficients of neighbor nodes. Semantic-level attention integrates semantic information into the representation of nodes by learning the optimal weighted combination of different meta-paths. Time-level attention is based on the time decay effect, and the time feature is introduced into the node representation by neighborhood formation sequence. Through the above three levels of attention mechanism, the final network embedding can be obtained.Through experiments on two real-world heterogeneous dynamic networks, our models have the best results, proving the effectiveness of the HDGAN model.

Community preserving adaptive graph convolutional networks for link prediction in attributed networks

Community detection in network data aims at grouping similar nodes sharing certain characteristics together. Most existing methods focus on detecting communities in undirected networks, where similarity between nodes is measured by their node features and whether they are connected. In this article, we propose a novel method to conduct network embedding and community detection simultaneously in a directed network. The network embedding model introduces two sets of vectors to represent the out- and in-nodes separately, and thus allows the same nodes belong to different out- and in-communities. The community detection formulation equips the negative log-likelihood with a novel regularization term to encourage community structure among the nodes representations, and thus achieves better performance by jointly estimating the nodes embeddings and their community structures. To tackle the resultant optimization task, an efficient alternative updating scheme is developed. More importantly, the asymptotic properties of the proposed method are established in terms of both network embedding and community detection, which are also supported by numerical experiments on some simulated and real examples.

Network embedding maps the nodes of a network to a continuous vector space, which can then be used as the input to downstream tasks, such as node classification, node clustering, link prediction, and similarity search. To learn network embedding more effectively, many technologies adopt the approach of random walk to obtain the network structure. As the meta-path of heterogeneous networks emerges, network embedding will be equipped with more semantic interpretation. Consequently, various random walks, based on meta-path strategies, have been proposed for network embedding. However, the combination of semantic and structure in a heterogeneous network cannot achieve ideal results. To overcome this challenge, we start from a task-guided issue by combining the timestamps information in the heterogeneous network, and then employing the method of temporal segmentation to decompose the network into a continuous temporal sequence. Finally, the set of context-paths between nodes is calculated in a continuous vector by the depth-first meta-path search algorithm. More precisely, we propose a Temporal Sliding Density Walk (TSDW) algorithm by combining network semantics and structure effectively. Empirical results for network data show that TSDW could significantly outperform the state-of-the-art representation learning models, including DeepWalk, LINE, Node2vec, PTE, Meapath2vec, HIN2vec, HTNE, and CTDNE by 3.02% to 44.9% of Macro-F1, 0.9% to 18.92% of Micro-F1 in multi-class node classification and 21% to 47% of NMI in node clustering.

Community detection has gained significant research interest within the data mining field. It involves identifying subsets of nodes with dense internal connections and sparse external connections. Most studies on community detection focus solely on identifying non-overlapping communities in a static graph. However, in practice, communities often overlap, and the structure of the graphs is dynamically evolving. This dynamic nature leads to community changes and poses a significant challenge in detecting overlapping communities on temporal graphs (T-OCD). While graph neural networks have shown great performance in generating node representations for community detection, learning representations that capture temporal graph structures and support overlapping community detection remain an open question. To address these challenges, we present T-OCDIB , a novel approach for T emporal O verlapping C ommunity D etection guided by I nformation B ottleneck. Specifically, we first propose an overlapping community detection approach for static graphs, under the guidance of a community-oriented information bottleneck. This approach allows us to learn discriminative node representations specific to each community, facilitating the detection of overlapping communities. Following this, we extend this method to temporal graphs by presenting a temporal convolution module. This module uses adaptive weight matrices based on evolving graph structures to capture temporal dependencies for community detection. Additionally, to promote smooth transitions between consecutive communities, we introduce a temporal smoothing module to further constrain changes in community structure. We evaluate the proposed approach on both real-world and synthetic temporal networks. Experimental results illustrate the superiority of T-OCDIB over other community detection methods.

Multi-relational community detection is a very important task in social network analysis because in the real world social networks are mostly multi-relational. In this paper, we propose a user-dependent method to detect communities in multi-relational social networks. We define a multi-relational community as a shared community over multiple single-relational graphs while the quality of a partitioning of nodes is assessed by a multi-relational modularity, and we design a desirable set of communities to represent the requests of users and use Normalized mutual information (NMI) between the desirable set of communities and the sets of communities detected in each single-relational graph as the weights for measuring the importance of all kinds of relationship types. We then use a greedy agglomerative manner to identify communities. Experiments have been conducted on synthetic networks to evaluate the effectiveness of the proposed approach.

Recent research on community detection focuses on learning representations of nodes using different network embedding methods, and then feeding them as normal features to clustering algorithms. However, we find that though one may have good results by direct clustering based on such network embedding features, there is ample room for improvement. More seriously, in many real networks, some statisticallysignificant nodes which play pivotal roles are often divided into incorrect communities using network embedding methods. This is because while some distance measures are used to capture the spatial relationship between nodes by embedding, the nodes after mapping to feature vectors are essentially not coupled any more, losing important structural information. To address this problem, we propose a general Markov Random Field (MRF) framework to incorporate coupling in network embedding which allows better detecting network communities. By smartly utilizing properties of MRF, the new framework not only preserves the advantages of network embedding (e.g. low complexity, high parallelizability and applicability for traditional machine learning), but also alleviates its core drawback of inadequate representations of dependencies via making up the missing coupling relationships. Experiments on real networks show that our new approach improves the accuracy of existing embedding methods (e.g. Node2Vec, DeepWalk and MNMF), and corrects most wrongly-divided statistically-significant nodes, which makes network embedding essentially suitable for real community detection applications. The new approach also outperforms other state-of-the-art conventional community detection methods.

Due to the power of learning representations from unlabeled graphs, graph contrastive learning (GCL) has shown excellent performance in community detection tasks. Existing GCL-based methods on the community detection usually focused on learning attribute representations of individual nodes, which, however, ignores structure semantics of communities (e.g., nodes in the same community should be structurally cohesive). Therefore, in this paper, we consider the community detection under the community structure semantics and propose an effective framework for graph contrastive learning under structure semantics (GCLS2) to detect communities. To seamlessly integrate interior dense and exterior sparse characteristics of communities with our contrastive learning strategy, we employ classic community structures to extract high-level structural views and design a structure semantic expression module to augment the original structural feature representation. Moreover, we formulate the structure contrastive loss to optimize the feature representation of nodes, which can better capture the topology of communities. To adapt to large-scale networks, we design a high-level graph partitioning (HGP) algorithm that minimizes the community detection loss for GCLS2 online training. It is worth noting that we prove a lower bound on the training of GCLS2 from the perspective of the information theory, explaining why GCLS2 can learn a more accurate representation of the structure. Extensive experiments have been conducted on various real-world graph datasets and confirmed that GCLS2 outperforms nine state-of-the-art methods, in terms of the accuracy, modularity, and efficiency of detecting communities.

Community detection is an effective approach to unveil relationships among individuals in online social networks. In the literature, quite a few algorithms have been proposed to conduct community detection by exploiting the topology of social networks and the attributes of social actors. In practice, community detection is usually conducted by third parties, such as advertisement companies and hospitals, with access to social networks for different purposes, which can easily lead to a privacy breach. In this paper, we investigate community detection in social networks aiming to protect the privacy of both the network topology and the users' attributes. We show that with additional prior knowledge, community detection can be performed by querying the information of only a fraction of instead of the entire population. In particular, we first propose a new scheme called differentially private community detection (DPCD). DPCD detects communities in social networks via a probabilistic generative model, which can be decomposed into subproblems solved by individual users. The private social relationships and attributes of each user are protected by objective perturbation with differential privacy guarantees. Then, we propose a parsimonious node affiliation recovery (NAR) algorithm, which is also differentially private, to unveil the community affiliation information of the whole population based on that of the limited number of queried individuals by solving a sparse optimization problem. Through both theoretical analysis and experimental validation using synthetic and real-world social networks, we demonstrate that the proposed DPCD scheme detects social communities under the modest privacy budget. In addition, we show the effectiveness of NAR to perform community detection by querying a limited number of individuals in social networks.

Exploring and understanding the temporal structure of dynamic networks attract extensive attention over the past few years. Most of these current research focuses on temporal community detection, evolution analysis or link prediction from a mission-oriented perspective. In fact, these three tasks should be not isolated but mutually reinforcing. Transforming these three tasks into a unified framework, it is crucial to extract the evolution pattern, which helps to understand the time-varying characteristics of temporal structure in essence. In addition, to the best of our knowledge, there is no work focusing on modeling and uncovering the local and global evolution pattern hidden in temporal community structure, simultaneously. In this paper, we propose a novel framework based on Orthogonal Nonnegative Matrix Factorization to Explore the Evolution Pattern (ONMF-EEP) for analyzing and predicting the time-varying structures in dynamic networks from local and global perspectives. The nature of this framework assumes that community structures are subject to a local evolution pattern (LEP) at each snapshot, and these LEPs are from a common global evolution pattern (GEP). The framework can synchronously detect temporal community structure, extract evolution pattern, and predict structure including communities and future snapshot links. The extensive experiments on real-world networks and artificial networks demonstrate that our proposed framework is highly effective on the tasks of dynamic network analysis.

Firstly, this paper selects multiple urban agglomerations to construct the network relationship of urban agglomerations from the three dimensions of transportation, economy and information. Secondly, it uses the community detection called Louvain algorithm to detect the community structure, focusing on the internal and external research of the community structure and based on NMI (Normalized Mutual Information) index for analysis and comparison. The results show that some cities have special positioning, which have different development space in the same types of network or different types of networks. For example, Hefei mainly play the role of high-speed rail collection and distribution within the urban agglomeration, and mainly play the role of high-speed distribution externally, while other cities such as Qianjiang do the opposite. Cities such as Yueyang are closely related to inner cities in the transportation dimension, but they are closely related to the outer cities in the economic or information dimension. Secondly, spatial distance has an impact on the phenomenon of community structure. Although spatial distance is not the sole factor influencing the closeness of urban agglomerations, it can be combined with the positioning of the urban agglomeration and the actual development situation to affect the phenomenon of the community structure. Thirdly, based on the comparison with the NMI analysis of the national policy urban agglomeration community structure, it is found that transportation not only promotes the development of the regional economy, but also promotes the formation of urban agglomerations. The community detection results from the perspective of the traffic dimension and the national policy urban agglomeration classification Relatively most consistent.KeywordsUrban trafficCommunity structureLouvain algorithmNMI

Identification of semantic community structures is important for understanding the interactions and sentiments of different groups of people and predicting the social emotion. A robust community detection method needs to autonomously determine the number of communities and community structure for a given network. Nonnegative matrix factorization (NMF), a component decomposition approach for latent sentiment discovery, has been extensively used for community detection. However, the existing NMF-based methods require the number of communities to be determined a priori , limiting their applicability in practice of affective computing. Here, we develop a novel NMF-based method to autonomously determine the number of semantic communities and community structure simultaneously. In our method, we use an initial number of semantic communities, larger than the actual number, in the NMF formulation, and then suppress some of the communities by introducing an adaptively weighted group-sparse low-rank regularization to derive the target number of communities and at the same time the corresponding community structure. Our method not only maintains the efficiency without increasing the complexity compared to the original NMF method but also can be straightforwardly extended to handle the non-network data. We thoroughly examine the new method, showing its superior performance over several competing methods on synthetic and large real-world social networks.

Community structures are fundamental in understanding the structure and functionality of complex networks. Different optimization algorithms, including both single-objective and multi-objective approaches, have been employed to address the challenge of community detection. Recently, multi-objective evolutionary algorithms (MOEAs) have attracted many researchers to identify communities in static networks. Many algorithms have been proposed to find a solution that achieves a trade-off between exploring new areas of the solution space and improving the quality of existing solutions. In this trade-off is crucial; whereas exploitation improves existing solutions, it may fail to find better solutions from insufficiently explored regions of the solution space. Therefore, mutation in evolutionary algorithms greatly impacts community detection within social networks. Conventional mutation methods usually tend to apply too much randomness, which results in convergence being less precise about finding a suitable optimum solution. This paper introduces a new mutation called community strength enhancement (CSE) to enhance the search efficiency of the Multi-Objective Evolutionary Algorithm with Decomposition (MOEA/D) and speed up the convergence of the suggested algorithm. Moreover, the proposed algorithm overcomes the limitations of traditional MOEA/D by accurately and effectively identifying communities across a wide range of social networks. The enhanced algorithm was evaluated on two groups of datasets (twenty synthetic and four real-world) using normalized mutual information (NMI) and modularity (Q) across five baseline models. Integrating the CSE mutation strategy led to significant improvements in performance, particularly under high mixing parameters and in large-scale networks, as evidenced by increased NMI and modularity scores

Complex networks, community structure, and catchment classification in a large-scale river basin