Most network embedding (NE) methods are either based on the proximity for community-guided tasks or on the structural similarity for role-oriented tasks. While being prevalent and effective, there still exists some potential issues that need further attention: 1) community and role are always regarded as orthogonal problems. They have rarely been combined to model the latent structures within the complex network. However, the generation of the network is usually jointly driven by these two mechanisms; and 2) few works study the interaction between roles or communities, which leads to the generation process of the network cannot being effectively modeled. To solve these problems, we propose a unified network embedding framework via mutual fusion of community and role (UMFCR). We combine the Gaussian mixture model (GMM) with a variational graph auto-encoder to generate node embeddings and discover the membership distribution of each node. An elaborate fusion pattern is then designed to produce the generation process for each link from the perspective of both community and role. The promising experimental results on real-world data demonstrate the necessity of fusing these two mechanisms and the superior performance of the model on different network tasks.

Information diffusion and diffusion prediction have attracted a great deal of research attention over the past decades. Existing approaches usually make predictions based on the order of the activated users, while recently, some studies have taken the social network into consideration and begun to analyze the influence of neighbors via some graph neural networks. However, they ignore the fact that the interests of users and their neighbors may dynamically change along with the growth of the cascade, and thus fail to model the potential impact of activated users. To address the above shortcomings, we proposed in this paper a deep learning model that combines theMode of cascadesGrowth and potentialImpact of users (MGI). It leverages GCNs to represent users from the social network to model their static features. Besides, we designed an attention mechanism on the cascade sequence to compute features of activated users, and added the popularity variable to model features of users in cascades. Finally, we combined the growth of cascades and impact of users in our model for diffusion prediction. We conducted extensive experiments on several real-world datasets, and the experimental results demonstrate that our model significantly outperforms the state-of-the-art methods in diffusion prediction.

Information diffusion prediction plays a crucial role in understanding the propagation of information in social networks, encompassing both macroscopic and microscopic prediction tasks. Macroscopic prediction estimates the overall impact of information diffusion, while microscopic prediction focuses on identifying the next user to be influenced. While prior research often concentrates on one of these aspects, a few tackle both concurrently. These two tasks provide complementary insights into the diffusion process at different levels, revealing common traits and unique attributes. The exploration of leveraging common features across these tasks to enhance information prediction remains an underexplored avenue. In this paper, we propose an intuitive and effective model that addresses both macroscopic and microscopic prediction tasks. Our approach considers the interactions and dynamics among cascades at the macro level and incorporates the social homophily of users in social networks at the micro level. Additionally, we introduce adversarial training and orthogonality constraints to ensure the integrity of shared features. Experimental results on four datasets demonstrate that our model significantly outperforms state-of-the-art methods.

Roles are defined as the equivalent classes of isomorphic nodes in the network. They focus on the local connective patterns and describe the structural similarities between nodes, and learning role-based network embeddings can help to recognize identities or functions of entities in real-world networks. This field has been studied over the past decades, however, the existing role-based network embedding methods all concentrate too much on distinguishing node structures and ignore that nodes can belong to different roles even if they have the same local structures. Not only the classical network structure can influence the role of node, but also the emergence of different type of relationship between nodes has impact to it. We believe that roles are influenced by multiple independent factors, and nodes in the same roles should possess both similar local structures and entangled patterns with neighbors hidden in each factor, but most of the existing methods did not clearly point out this challenge. Therefore, we propose a disentangled framework based on graph neural networks to simultaneously model the local structures and interactive relationships in multiple factors to generate role-oriented network embeddings. We design a novel role-aware neighbor choosing mechanism to assign each neighbor a different interactive weight for each latent factor, which can measure its influence on roles. We conduct experiments on synthetic and real-world networks, and the results demonstrate the superiority and effectiveness of our model.

Capturing structural similarity has been a hot topic in the field of network embedding (NE) recently due to its great help in understanding node functions and behaviors. However, existing works have paid very much attention to learning structures on homogeneous networks, while the related study on heterogeneous networks is still void. In this article, we try to take the first step for representation learning on heterostructures, which is very challenging due to their highly diverse combinations of node types and underlying structures. To effectively distinguish diverse heterostructures, we first propose a theoretically guaranteed technique called heterogeneous anonymous walk (HAW) and give two more applicable variants. Then, we devise the HAW embedding (HAWE) and its variants in a data-driven manner to circumvent using an extremely large number of possible walks and train embeddings by predicting occurring walks in the neighborhood of each node. Finally, we design and apply extensive and illustrative experiments on synthetic and real-world networks to build a benchmark on heterostructure learning and evaluate the effectiveness of our methods. The results demonstrate our methods achieve outstanding performance compared with both homogeneous and heterogeneous classic methods and can be applied on large-scale networks.

Recently, network embedding (NE) is an amazing research point in complex networks and devoted to a variety of tasks. Nearly, all the methods and models of NE are based on the local, high-order, or global similarity of the networks, and few studies have focused on the role discovery or structural similarity, which is of great significance in spreading dynamics and network theory. Meanwhile, existing NE models for role discovery suffer from two limitations, that is: 1) they fail to model the varying dependencies between each node and its neighbor nodes and 2) they cannot capture the effective node features which are helpful to role discovery, which makes these methods ineffective when applied to the role discovery task. To solve the above problems of NE for role discovery or structural similarity, we propose a unified deep learning framework, called RDAA, which can effectively represent features of nodes and benefit the Role Discovery-guided NE with a deep autoencoder, while modeling the local links with an Attention mechanism. In addition, we design an elaborately binding technique to combine both parts and optimize the framework in a unified way. We conduct different experiments, including visualization, role classification, role discovery, and running time compared to popular NE methods for both proximity and structural similarity. The RDAA has better performance on all the datasets and achieves good tradeoffs.

Recently, Network Embedding (NE) has become one of the most attractive research topics in machine learning and data mining. NE approaches have achieved promising performance in various graph mining tasks including link prediction and node clustering and classification. A wide variety of NE methods focus on the proximity of networks, they learn community-oriented embedding for each node, where the corresponding representations are similar if two nodes are closer to each other in the network. Meanwhile, there is another type of structural similarity, i.e., role-based similarity, which is completely different from and complementary to the proximity. In order to preserve the role-based structural similarity, the problem of role-oriented NE is raised. However, compared to the community-oriented NE, there are only a few role-oriented embedding approaches proposed recently. Although less explored, considering the importance of roles in analyzing networks and many applications that role-oriented NE can shed light on, it is necessary and timely to provide a comprehensive overview of existing role-oriented NE methods. In this review, we first clarify the differences between community-oriented and role-oriented network embedding. Afterward, we propose a general framework for understanding role-oriented NE and a two-level categorization to better classify existing methods. Then, we select some representative methods according to the proposed categorization and briefly introduce them by discussing their motivation, development, and differences. Moreover, we conduct comprehensive experiments to empirically evaluate these methods on a variety of role-related tasks including node classification and clustering (role discovery), top-k similarity search, and visualization using some widely used synthetic and real-world datasets. Finally, we further discuss the research trend of role-oriented NE from the perspective of applications and point out some potential future directions.

Roles of nodes are defined as classes of equivalent nodes. Nodes that have similar local connective patterns may share the same role. As a complementary concept of community, role can also help to recognize real-world entities. For example, it can denote identity or function in social networks. Role has been studied over the past decades, and learning role-based network representations is crucial to many downstream tasks. The important step for role-based network embedding method is extracting features to measure structural similarity instead of proximity. Although some methods have been developed to capture role features to learn structural similarities between nodes, they all design these features of fixed types, such as the global, local, and higher-order features. These features can only represent a certain type of structure, and it is very difficult to model the complex relationship between different scale features in the field of role-based network embedding. Therefore, we propose a novel role-oriented network embedding framework based on adversarial learning between higher-order and local features (ARHOL) to generate powerful role-based node representations. The higher-order features are discrete so we leverage the Auto-Encoder on them to obtain continuous representations. Then we apply the GIN on its outputs to aggregate local information. Finally, we consider the GIN as the generator and design an adversarial game between local features and GIN outputs to integrate these two aspects of features, which can enhance each other and improve the robustness. The extensive experiments on real-world networks demonstrate the superiority and efficiency of our model, and prove the effectiveness of integrating higher-order and local features.

Role of node is defined on structural similarity or local connective pattern, describing the functions of node in the network. In real-world situation, it can denote person’s identity and status. It has been studied over the past decades, and learning role-based network representations is crucial to many downstream tasks. In this field, the important step for is extracting some measurements to evaluate structural similarity. Although some methods have been developed to capture the role features to learn the structural similarities between nodes, they all design the features of fixed types, such as global, local, and higher-order features. These features can only discover single type of roles, and simply combing them may cause damage to performance. It is very difficult to model the complex relationship between different scale features in the field of role-based network embedding. Therefore, we propose a novel adversarial framework to generate structural node representations via higher-order features and adversarial learning (SHOAL). We leverage the Auto-Encoder on higher-order features and some GNNs on its outputs to aggregate local neighbors. We believe that higher-order and local features can denote roles, and effectively integrating them will help for role discovery. So we consider the GNNs as the generator and design an adversarial game between these features, which can also improve the robustness. The experiments on real-world networks demonstrate the superiority and efficiency of our model, and the results also prove the effectiveness of integrating higher-order and local features.

Role-based network embedding methods aim to preserve node-centric connectivity patterns, which are expressions of node roles, into low-dimensional vectors. However, almost all the existing methods are designed for capturing a relaxation of automorphic equivalence or regular equivalence. They may be good at structure identification but could show poorer performance on role identification. Because automorphic equivalence and regular equivalence strictly tie the role of a node to the identities of all its neighbors. To mitigate this problem, we construct a framework called Curvature-based Network Embedding with Stochastic Equivalence (CNESE) to embed stochastic equivalence. More specifically, we estimate the role distribution of nodes based on discrete Ricci curvature for its excellent ability to concisely representing local topology. We use a Variational Auto-Encoder to generate embeddings while a degree-guided regularizer and a contrastive learning regularizer are leveraged to improving both its robustness and discrimination ability. The effectiveness of our proposed CNESE is demonstrated by extensive experiments on real-world networks.