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Great achievements have been made in network embedding based on single-layer networks. However, there are a variety of scenarios and systems that can be presented as multiplex networks, which can reveal more interesting patterns hidden in the data compared to single-layer networks. In the field of network embedding, in order to project the multiplex network into the latent space, it is necessary to consider richer structural information among network layers. However, current methods for multiplex network embedding mostly focus on the similarity of nodes in each layer of the network, while ignoring the similarity between different layers. In this paper, for multiplex network embedding, we propose a Layer Information Similarity Concerned Network Embedding (LISCNE) model considering the similarities between layers. Firstly, we introduce the common vector for each node shared by all layers and layer vectors for each layer where common vectors obtain the overall structure of the multiplex network and layer vectors learn semantics for each layer. We get the node embeddings in each layer by concatenating the common vectors and layer vectors with the consideration that the node embedding is related not only to the surrounding neighbors but also to the overall semantics. Furthermore, we define an index to formalize the similarity between different layers and the cross-network association. Constrained by layer similarity, the layer vectors with greater similarity are closer to each other and the aligned node embedding in these layers is also closer. To evaluate our proposed model, we conduct node classification and link prediction tasks to verify the effectiveness of our model, and the results show that LISCNE can achieve better or comparable performance compared to existing baseline methods. [ABSTRACT FROM AUTHOR]

Representation learning for dynamic networks is designed to learn the low-dimensional embeddings of nodes that can well preserve the snapshot structure, properties and temporal evolution of dynamic networks. However, current dynamic network representation learning methods tend to focus on estimating or generating observed snapshot structures, paying excessive attention to network details, and disregarding distinctions between snapshots with larger time intervals, resulting in less robustness for sparse or noisy networks. To alleviate these challenges, this paper proposes a contrastive mechanism for temporal representation learning on dynamic networks, inspired by the success of contrastive learning in visual and static network representation learning. This paper proposes a novel Dynamic Network Contrastive representation Learning (DNCL) model. Specifically, contrast objective functions are constructed using intra-snapshot and inter-snapshot contrasts to capture the network topology, node feature information, and network evolution information, respectively. Rather than estimating or generating ground-truth network features, the proposed approach maximizes mutual information between nodes from different time steps and views generated. The experimental results of link prediction, node classification, and clustering on several real-world and synthetic networks demonstrate the superiority of DNCL over state-of-the-art methods, indicating the effectiveness of the proposed approach for dynamic network representation learning. • We propose a novel approach to dynamic network representation learning by applying contrastive learning. • DNCL design dynamic contrastive objective to capture the temporal and topological features of dynamic networks. • DNCL's objective consists of inter-snapshot contrast and intra-snapshot contrast. • DNCL achieves state-of-the-art performance compared with the base-lines on tasks. [ABSTRACT FROM AUTHOR]

Abstract Temporal community detection could help us analyze and understand the meaningful substructure hidden within dynamic networks in the real world. Evolutionary clustering, as a popular framework for clustering stream data, has been denoted for mining the communities in dynamic networks. However, most of these methods ignore the varying characteristics of micro structure of the networks and lack of statistical interpretation. In this paper, we propose a powerful, interpretable and extensible evolutionary clustering framework based on nonnegative matrix factorization (NMF) for temporal community detection via combining the first-order varying information of micro structure in dynamic networks from the perspective of statistical model. Firstly, we consider the first-order varying information of nodes by constructing a temporal similarity matrix over time. Secondly, we present the framework, FVI-NMF, for detecting temporal community based on NMF combining the First-order Varying Information. Thirdly, we develop a effective algorithm to optimize the objective function of FVI-NMF and analyze its complexity. In addition, our model can discover the evolutionary pattern of temporal communities synchronously, which has a variety applications in the analysis of dynamic network. Experiments on both artificial and real dynamic networks demonstrate that our proposed framework has superior performance in comparison with state-of-art methods. Highlights • A powerful framework FVI-NMF for temporal community detection is proposed. • FVI-NMF combines historical structures with the varying characteristics of micro structure. • FVI-NMF could uncover the temporal evolutionary pattern of communities. [ABSTRACT FROM AUTHOR]

Heterogeneous Information Networks (HINs) are commonly employed to model complex real-world scenarios with diverse node and edge types. However, due to constraints in data collection and processing, constructed networks often lack certain relations. Consequently, various methods have emerged, particularly recently, leveraging heterogeneous graph neural networks (HGNNs) to predict missing relations. Nevertheless, these methods primarily focus on pairwise relations between two nodes. Real-world interactions, however, often involve multiple nodes and diverse types, extending beyond simple pairwise relations. For instance, academic collaboration networks may entail interactions among authors, papers, and conferences simultaneously. Despite their prevalence, higher-order relations are often overlooked. While HGNNs are effective at learning network structures, they may suffer from over-smoothing, resulting in similar representations for nodes and their neighbors. The learned inaccurate proximity among nodes impedes the discernment of higher-order relations. Furthermore, observed edges among a target group of nodes can provide valuable evidence for predicting higher-order relations. To address these challenges, we propose a novel model called Accurate Neighborhood- and Self-information Enhanced Heterogeneous Graph Neural Network (ANSE-HGN). Building upon HGNNs to encode network structure and attributes, we introduce a relation-based neighborhood encoder to capture information within multi-hop neighborhoods in heterogeneous higher-order relations. This enables the calculation of accurate proximity among target groups of nodes, thereby enhancing prediction accuracy. Additionally, we leverage self-information from observed higher-order relations as an auxiliary loss to reinforce the learning process. Extensive experiments on four real-world datasets demonstrate the superiority of our proposed method in higher-order relation prediction tasks. • We propose ANSE-HGN to solve the problem of higher-order relation prediction in HINs. • We accurately capture the proximity of higher-order relations by multi-hop neighbors. • We design a self-information loss to assist in model optimization. • We conduct experiments on four datasets, demonstrating the effectiveness of ANSE-HGN. [ABSTRACT FROM AUTHOR]

Network alignment plays an important role in many fields. The main task of network alignment is to find the node correspondence between different networks, i.e. whether they represent the same natural entity. Most existing alignment methods obtain the relevant information of nodes in the network through network representation learning technology, and then calculate the relationship between different nodes based on the node representations. These methods mostly focus on Euclidean geometry to learn node representations, does Euclidean space fit well with the network alignment? Considering that real-world networks often exhibit hierarchical structure and hyperbolic geometry shows the advantage of expressing network hierarchical structure, some researchers use hyperbolic geometry to learn node representations. But the network is not all hierarchical structure, so we exploit Euclidean and hyperbolic geometries jointly for node representation learning through an interactive learning mechanism to exploit the reliable spatial features in networks. The proposed method can well adapt to the complex structure in the network, providing efficient node representations for network alignment. Extensive experiments on synthetic and real-world datasets show the superiority of our method for network alignment. [ABSTRACT FROM AUTHOR]

Link prediction in bipartite networks aims to identify or predict possible links between nodes of different types based on known network information. However, most existing studies predominantly focus on monopartite networks, neglecting the intrinsic properties unique to bipartite networks, such as the intricate high-order relationships between nodes. Both explicit relations (representing low-order information) and implicit relations (representing high-order information) play essential roles in predicting the evolution of bipartite networks, and they are indispensable and mutually reinforce each other. To fully leverage their potential in addressing the link prediction problem, we propose a novel framework from the perspective of network representation. This framework not only effectively integrates explicit relations and implicit relations, but also preserves the local and global structure of bipartite networks. Specifically, the probability of a link between two nodes of different types is determined by the linear sum of the contribution values of the mutually connected nodes in their respective common neighbors. Implicit relations are then used to preserve the local structure during the network representation. Furthermore, we implement optimization using a relaxed majorization-minimization algorithm, offering the advantage of uncovering high-quality local minima. Our proposed framework has undergone extensive testing on eight real-world datasets, and the results unequivocally demonstrate its significant superiority over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Role-based network embedding aims to map network into low-dimensional node representations while preserving structural similarities. Adjacency matrix contain both the local and global information of a network, but it cannot directly represent the role of nodes. So it is essential to extract higher-order structural features from adjacency matrix for role-based network embedding (structural equivalence). While being sensitive to noise in real networks in general, the features extracted by some identical methods cannot truly represent the role of nodes. Therefore, we propose a deep learning framework RESD. In detail, we first propose extracting higher-order structural features for each node in the network. Then, we utilize the Variational Auto-Encoder (VAE) to model the nonlinear relationship of the features, reduce noise and improve the robustness of embedding. Furthermore, in the embedding space, we apply a degree-regularized constraint to guide the representation learning for preserving key structural information of nodes (e.g., degrees), which may be lost due to the principle of VAE framework. Finally, we construct a unified objective function to learn the node embedding for role discovery by preserving the structural features and node degree. We compare our model with several state-of-the-art methods on real-world networks. The results of extensive experiments demonstrate the effectiveness of our model and prove that our model scales well with dimension and network size. [ABSTRACT FROM AUTHOR]