A heterogeneous network G = ( V , E ; O V , R E , A V ) with two types of nodes V, three types of links E, and node attributes A _V is defined. In Figure 1B, O _V includes user node U (round), event nodes E (square), and V = U ∪ E; R _E includes user–event relation R _ue , event–event relation R _ee , user–user relation R _ue , and E = R _ue ∪ R _ee ∪ R _uu . A _V is the attribute feature of the node, including the semantic attribute A V S (rectangle) and topology attribute A V T . For user u, its r-neighbors are defined to be Γ u r = { v : d ( v , u ) < = r } , where d (v, v _u ) is the distance (number of hops) from v to u, and v is different types of nodes in heterogeneous subgraph G. The r-ego heterogeneous subgraph of user u is the local heterogeneous subgraph induced by Γ u r and denoted by G u r .

Social action refers to the behavior of users in the social network events, such as social network users retweet tweets (events) or publish papers (events). Formally, a social action can be regarded as the action of user u on event e at time t in the heterogeneous graph G _u . We define social action as a binary problem. Action status S u e t belongs to (0,1). When S u e t = 1 , it means that user u has social action for an event e after time t; when S u e t = 0 , it means that no social action has occurred.

Social influence locality models the probability of social action when ego-user u _i is influenced by neighbor nodes on his r-ego network G u i r ; formally, given a 6-tuple {u, e, t, G, A, S}, social influence locality aims to quantify the activation probability of user u _i ’s social action in response to event e after a given time t in G with attribute feature A and action status S as follows: p r o b ( S u i t + Δ t | e j t , G u i r , A G t , S G t ) , (1) where u _i represents the ego-user, e j t represents the event e _j at time t, G u i r represents r-heterogeneous neighbor subgraph, A G t represents the node attributes by time t, including semantic attribute A ^S , topology attribute A ^T , and S G t represents the action state of the subgraph node before timestamp t.

After determining the problem, we sample N 6-tuple samples through preprocessing data. Similar to the definition of DeepInf [14], we regard social influence locality as a binary classification problem and calculate the model parameters by minimizing the negative log likelihood objective method. We use the following objective with parameters θ: L ( θ ) = − ∑ j = 1 M ∑ i = 1 N ( S u i t + Δ t | e j t , G u i r , A G t , S G t ) . (2)

Similarly, we assume that time Δt is infinite, that is, we only predict user action outside the observation time window.

Generally, the graph neural network uses the feature information of the node’s n-order neighbor (e.g., first older) for the aggregation process of node features, such as GAT [19]. Therefore, the breadth first search (BFS) strategy [25] used in the graph localization process will make the weight between users and events too large in hot events. For example, in popular events, due to a large number of related events, most of the neighbor nodes sampled by a user are event type nodes, which will lead to the event type nodes becoming the dominant influence, and ignore the influence between users. In order to solve this problem, an improved random walk strategy was used to comply with the law of information dissemination. The sampling strategy includes two steps:

1. Sample a fixed-length random walk sequence. We took each user u ∈ U as the starting point, utilizing the RWR [17] method to sample a fixed number of N _r neighbor nodes.

This strategy satisfies the law of information dissemination and helps avoid the problem of too little sampling of some types of nodes. Similar to the definition in DeepInf [14], a positive instance of a local heterogeneous subgraph was generated if a user has social action with an event after the timestamp t, and a negative instance was generated if the user is not observed in the watch window to be associated with the event.

In this way, 6-tuple (2.3) was used as a set of examples and a deep learning model was designed to predict the action state S u t + Δ t of the ego-user. Our neural network model consists of three parts: a semantic feature aggregation module (shown in Figure 2c-1), topological feature aggregation module (shown in Figure 2c-2), and heterogeneous multi-attribute hidden layer aggregation module (shown in Figure 2c-3). In this section, the different modules are introduced to express the process of model building.

Following the previous studies [14], experiments on two public datasets were conducted to quantitatively evaluate our proposed model. The detailed statistics are presented in Table 1.

Digg [29]: The Digg dataset is a story collector, which contains the data of stories that were promoted to Digg home page within 1 month in 2009. For each story, this dataset collects the voting lists of all users, the voters’ friendship links, and the timestamp of each vote. This dataset comes from the study in reference 30. In our experiment, we took the story as the “event” node and “voting” as the user action to build a heterogeneity graph. Due to the lack of text data in the dataset, the deep framework (Figure 2c-2) of semantic information was not used in this dataset.

Weibo [31]: Weibo is the most popular social networking platform in China. This dataset contains 3,000,000 original tweets and retweets and comments of the original tweets from September 28, 2012 to October 29, 2012. At the same time, the dataset also contains the follow relationship between users who participate in these tweets. The dataset comes from in the study in reference 32. In our experiment, we extracted hashtags as events and built the heterogeneous graph of users and events, and the behavior of users participating in events (comment or retweet) is regarded as user action.

In view of the imbalance in the number of active neighbors proposed by DeepInf, we set a threshold n > 5 (n is the sum of the number of active users and active events).Therefore, less active observation samples are removed, and thus, the sample characteristics involved in training are significantly related to social influence [31]. In order to solve the problem of data skew, the down-sampling method was used to control the positive and negative ratio of samples at 1:3.

Compared with the previous study, the preparation has the following differences:

(1) For the choice of events, due to the shortcomings of the number of participants lack significance, we excluded some events with fewer participants and set the threshold of the number of participants to the top 30% of the distribution of the number of events so as to extract the total number of events in Table 1.

Support Vector Machine (SVM) [34]: A support vector machine (SVM) with linear kernel was used as the classification model. Specifically, the splicing of three features (including semantic features, topology features, and action status) was used as the input vector, and the problem was defined as two classification method.

DeepInf [14]: Our framework was compared with the influence network model based on the graph neural network, which constructs homogeneity subgraph based on user relationship and predicts user node action in the future.

MvInf [15]: Our framework was compared with the state-of-the-art graph neural network model MvInf, which introduces a multi-view structure based on DeepInf and uses the complementarity and consistency between different views to enhance learning performance. The difference is that our proposed model is based on the common influence of events and users.

HetInf and Its Variants: In the heterogeneous multi-attribute hidden layer aggregation module, different graph neural network frameworks were used to distinguish the two methods: HetInf–GCN and HetInf–GAT. Separately, HetInf–GAT uses the GAT [19] method as a method to fuse node features, mainly using attention mechanism to obtain the importance between nodes, while the HetInf–GCN method uses the GCN [27] framework to aggregate the node features and calculate the node influence by learning the node relationship of the subgraph.

In our proposed method, we used DeepWalk [24] to embed the node topology features; the restart probability of this method is 0.8, and the output vector length is 64 dimensions. We used the ReLU [35] as the activation function sigma (Eq. 5, 6) and used the Adam [36] optimizer for training, with a learning rate of 0.005, and we set dropout = 0.5. We used 50, 25, and 25% of the instances for training, validation, and testing respectively; the batch size of all datasets was set to 256. In order to accommodate more nodes, we set the total number of nodes in the subgraph to 100 (including two different types of nodes).

Social influence prediction is a fundamental problem in a social network analysis, which supports downstream tasks. At the micro-perspective [37,38], this problem is mainly modeled by analyzing user relationships. There are many different research directions, such as a user interaction influence analysis [39,40], network structure diversity analysis [41,42], topic influence analysis [10], and influence maximization [43]. Specifically, in the study in reference 44, the existence of social influence was proved by quantitative analysis of mutual influence. The study in reference 31 proposes social local network concepts, using user interaction and network structure to predict user behavior. The study in reference 45 uses topic level influence to model user influence. The study in reference 46 introduces a topic-level influence propagation and aggregation algorithm to derive the indirect influence between nodes. In recent years, with the continuous progress of deep learning, many studies have introduced deep learning into social influence prediction to improve the prediction performance. A popular deep learning method is [14], which provides an end-to-end framework to predict social influence by learning the potential features of users. The study in reference 15 has improved the study in reference 14 to enhance feature representation and result accuracy with a multi-view model. The study in reference 47 proposes a social influence prediction model NNMInf based on neural network multi-label classification. The study in reference 48 introduces a deep neural network framework witch simulate social influence and predict human behavior. Compared with traditional methods, these deep learning models show better learning performance.

In recent years, we have identified a huge development of the graph neural network in deep learning technology [27,49], and the state-of-the-art model GAT [19], which represents the method of depth learning-based graphical representation as the graph neural network (GNN), the main idea is as follows: the first step is to calculate the feature representation of neighbor nodes, and the second step is to aggregate neighbors through message passing mechanism to obtain the feature representation of nodes [50].

Recently, the heterogeneous graph neural network has become the main branch of GNN. The main task is to learn the representation of heterogeneous nodes on the graph neural network, so as to adapt to the downstream tasks based on heterogeneous networks. The study in reference 13 realizes node representation of heterogeneous networks by aggregating features of different types of nodes in stages. The study in reference 51 proposes a heterogeneous graph neural network based on hierarchical attention, including node level attention and semantic level attention. Node level attention aims to learn the importance between nodes and their neighbors based on meta-paths, while semantic level attention can learn the importance of different meta-paths. The study in reference 52 proposes a heterogeneous graph neural network method for subgraphs, which trains a classifier to learn the neighbor average features of the random sampling graph of the relational “metagraph.” The MAGNN [53] model which contains the node content transformation to encapsulate input node attributes, the intra-meta-path aggregation to incorporate intermediate semantic nodes, and the inter-meta-path aggregation to combine messages from multiple meta-paths. GTN [54], which generates new graph structures by identifying useful connections between unconnected nodes on the original graph, can learn effective node embeddings on the new graphs in an end-to-end fashion. HGNN-AC [55] based on reference 53 proposed a general framework for heterogeneous graph neural network via Attribute Completion, including pre-learning of topological embedding and attribute completion with attention mechanism. These heterogeneous graph neural network representation methods enhance the representation ability of nodes and provide a more practical idea for downstream tasks.