# CDSTAEP: Cross-Domain Spatial-Temporal Association Learning for Abnormal Events Prediction
## 2 Related Work  
Predictive analysis of behavioral events is not a new problem and has applications in different fields--for example, intelligent recommendation systems in social networks [23], traffic flow prediction in smart transportation [24], etc. The critical problem is the temporal-spatial association analysis of behavioral events. The CDSTAEP model in this paper uses the basic graph representation learning method to characterize the spatial correlation between events and nodes and uses the deep neural network with LSTM to predict abnormal events. Here, we briefly discuss the work related to the GNN for node, event correlation, and the prediction of abnormal events (behaviors) combined with time and space. **Network Embedding:** By defining operations such as approximate convolution, GNN is applied to graph information processing or complex network information processing. Symmetric models in Euclidean space cannot well represent complex data patterns, such as the underlying hierarchical and periodic structures in categorical data [12; 25]. Since graphs have the properties of non-Euclidean space, such as power-law distribution and potential hierarchical structure in essence, in recent years, the latest research results suggest that graph structure data be represented in Riemannian space, that is, the combination of GNN and Riemannian space representation learning [26; 27; 28] to represent hierarchical graph data. Where (1) in hyperbolic space, because it can represent a hierarchical data structure, especially a tree structure, and can retain more information than representation in Euclidean space, relevant research has proposed a shallow learning representation model [14; 29; 30]. With the emergence of massive structured data, the depth map neural network learning representation model (GNN) has been proposed [6; 31; 32; 33], and the model ACE-HGNN [12], which explores the optimal curvature of hyperbolic space, is also one of the recent outstanding achievements. In terms of the promotion and application of the hyperbolic space GNN, recent research uses the hyperbolic space representation model of the complex network to capture the characteristics of the hierarchical structure effectively. These models are used in the intelligent question-answering system [34], link prediction [35], and machine translation [25]. Compared with the high latitude European space, it has improved performance. In addition, the research result [36] extends hyperbolic GNN to a dynamic graph representation, which is used to infer the representation of random nodes and has original findings in the analysis of time dimension. (2) The representation of graph structure data in mixed-curvature space can better preserve the relationship and attributes of complex network data. To learn and optimize graph embedding in constant curvature space, [PERSON] [37] and others studied matrix manifolds in Riemannian space and captured various metrics of different graph attributes, and the results were better than hyperbolic embedding and elliptic embedding. Recently, some research has proposed a learning method of mixed-curvature representation based on Riemannian space [9; 16] to represent complex network nodes in Riemannian space. In constructing a knowledge map [38], the representation of mixed-curvature space also reflects its advantages in relation to the discovery. The comparison of network representation learning methods related to this study is shown in Table 1.  
Unlike the above research, we first construct the event association graph to obtain the high-dimensional representation of the event relationship and then learn the low-dimensional representation of the complex correlation relationship between events in the mixed-curvature space, to capture the spatial correlation relationship between cross-domain events. **Association Analysis of Abnormal Network Events:** It is usually relatively difficult to predict events or behaviors by combining temporal and spatial characteristics.