## 2 Proposed Method  
In order to improve the accuracy of PM\({}_{2.5}\) concentration prediction, an improved attention based dual-stage two-phase fully connected (DSTP-FC) model is proposed in this paper, which is used for central site PM\({}_{2.5}\) concentration prediction, and multi-site data are used as an input to help more accurately predict PM\({}_{2.5}\) concentration at a central site. The data of twelve air quality sites in Beijing, China are used to test the proposed model, which will be introduced in detail in Section 3.1. The locations of these twelve air quality sites are shown in Figure 1, where the location of the central site is represented by a red triangle in the figure.  
The inputs of the model include historical air quality and meteorological data. The data flow of the proposed method is shown in Algorithm 1.  
Firstly, the spatiotemporal correlations between the central site and the neighboring sites are analyzed, according to the correlations of the target series in two sites (that is PM\({}_{2.5}\) series), then the central site collection is set up. The locations of the neighboring sites are represented by yellow triangles in Figure 1.  
Secondly, the model selects one site with the highest correlation for all the sites in the central site collection from all other sites, according to the exogenous series correlation. Then the site pairs are obtained. The PM\({}_{2.5}\) prediction results of each site pair can be obtained by inputting all data of these site pairs into the improved dual-stage two-phase model based on the attention mechanism, respectively.  
Finally, the prediction results of all sites in these site pairs are input into the attention-based layer to get the prediction results of the central site.  
The framework of the proposed method is shown in Figure 2 and is described in detail below.  
Figure 1: Distribution of air quality sites in Beijing.  
```
0: All sites' data for current batch, denoted as \(P_{n}\);
0: The prediction result of the central site \(N_{0}\), denoted as \(S\); (1) Firstly, according to the target series of the central site and other sites, determine the relevant sites of the central site \(N_{0}\). Here are \(N_{1}\), \(N_{2}\), \(N_{3}\), \(N_{4}\). These five sites are called the central site collection; (2) Secondly, according to the exogenous series of the sites in the central site collection and other sites, the matching sites are determined by the exogenous series correlation method. Here are \(N_{best0}\), \(N_{best1}\), \(N_{best2}\), \(N_{best3}\), \(N_{best4}\) respectively; (3) Thirdly, the site pairs (\(N_{0}\), \(N_{best0}\)), (\(N_{1}\), \(N_{best1}\)), (\(N_{2}\), \(N_{best2}\)), (\(N_{3}\), \(N_{best3}\)), (\(N_{4}\), \(N_{best4}\)) are input into the model respectively to get the prediction results of the sites in the central site collection. The site pair (\(N_{i}\), \(N_{best_{i}}\)) contains the exogenous series and target series of these two sites. (4) Finally, with the prediction results of each site in the central site collection, the attention-based layer get the prediction result \(S\) of the central site; return\(S\);
```  
**Algorithm 1** The data flow of the proposed method