# A Hierarchical Generative Embedding Model for Influence Maximization in Attributed Social Networks
## 2 Related Work  
Influence Diffusion. The studies of influence diffusion focus on the key factors for influence diffusion, such as diffusion models of a single entity or multiple entities, as well as the influence probability between two nodes, which is more relevant to our work. Estimating influence probability between two nodes (or influence strength) is a fundamental problem for influence diffusion, since in real-world propagation scenarios, the variables such as influence strength and infection time may be not directly observed. Some models to estimate influence strength have been proposed. One line of research is based on topic extraction and lays emphasis on incorporating the topic model into influence diffusion. Ref. [15] proposes a latent variable model, which captures community-level topic interest, item-topic relevance and community membership distribution of each user and further infers user-to-user influence strength. Ref. [14] proposes a novel model, COLD, to model community-level influence diffusion. Another line of studies utilize various probabilistic methods such as Bayesian inference [16] and EM (Expectation maximization) [17] to stimulate influence diffusion and learn the parameters in the generative model. Recently, researchers have endeavored to build models of influence prediction using deep learning, which can predict social influence automatically and are no longer limited to expert knowledge when extracting user features or network features. Ref. [18] proposes a recurrent neural variational model (RNV) to dynamically track entity correlations and cascade correlations. Ref. [19] proposes the DeepInf model to predict social influence, which detects the dynamics of social influence and integrates network embedding and graph attention mechanisms into the model. Ref. [21] proposes a reinforcement learning framework to discover effective network sampling heuristics by leveraging automatically learned node and graph representations. To the best of our knowledge, the existing models to predict the influence probability between two nodes usually extracts features of user interactions with various humanly devised rules, which heavily depends on expert knowledge of this domain. Besides, the underlying factors that affect social network influence, such as communities, community tensility and node depth in a clustering tree, have not been taken into account in the existing models when computing the influence probability of node pairs. Moreover, the existing models are often applicable for special scenarios or specific diffusion models, not for generalized conditions. Network Embedding. Network embedding techniques aim at inferring representations, also called embeddings, of entities in the networks. The basic idea of network embedding is to embed the nodes into a low-dimensional vector space in which the similarity between nodes can be measured and network structures can be preserved as much as possible. Many downstream learning tasks can benefit from this form of representation, such as link prediction, node classification, node clustering and network visualization. Existing models of network embedding are concerned about the technology of mapping or dimension reduction. In order to obtain effective low-dimensional embeddings, numerous algorithms have been proposed. Inspired by Word2 Vec [22], deep learning has been migrated to network embedding. DeepWalk [23], Node2 Vec [24] and Line [25] extract a number of sequential nodes in the network by random walk. Nodes in a sequence are metaphorically equivalent to words in language models. Skip-Gram [22] is then employed to obtain the embeddings of nodes. After obtaining the embeddings of nodes, the similarity of nodes can be calculated by the inner-product of their embeddings. LINE [25] uses first-order and second-order proximities and trains the model via negative sampling. SDNE [26] adopts a deep auto-encoder to preserve both the first-order and second-order proximities.