# Construction of Air Quality Level Prediction Model Based on STEPDISC-PCA-BP
## 3 Results and Discussion
### PCA Method to Reduce the Factors Dimension
Based on the eigenvectors of the first five principal components and Equation (3), the expressions of the principal components can be written as follows:  
\[prin1=0.203\text{AP}^{*}-0.197\text{WS}^{*}-0.219\text{SH}^{*}+0.205\text{RH} ^{*}+0.402\text{PM}^{*}_{2.5}+0.194\text{PM}^{*}_{10}+0.457\text{SO}^{*}_{2}+0. 449\text{NO}^{*}_{2}+0.47\text{CO}^{*}\]  
\[prin2=-0.39\text{AP}^{*}+0.422\text{WS}^{*}+0.022\text{SH}^{*}-0.202\text{RH} ^{*}+0.456\text{PM}^{*}_{2.5}+0.635\text{PM}^{*}_{10}-0.107\text{SO}^{*}_{2}-0. 078\text{NO}^{*}_{2}-0.03\text{CO}^{*}\]  
\[prin3=-0.058\text{AP}^{*}-0.236\text{WS}^{*}+0.668\text{SH}^{*}-0.612\text{ RH}^{*}-0.030\text{PM}^{*}_{2.5}-0.007\text{PM}^{*}_{10}+0.182\text{SO}^{*}_{2}+0. 277\text{NO}^{*}_{2}+0.091\text{CO}^{*}\]  
\[prin4=0.83\text{AP}^{*}+0.221\text{WS}^{*}-0.106\text{SH}^{*}-0.363\text{RH} ^{*}-0.002\text{PM}^{*}_{2.5}+0.233\text{PM}^{*}_{10}+0.081\text{SO}^{*}_{2}-0.18\text{NO}^{*}_{2}-0.161\text{CO}^{*}\]  
\[prin5=-0.07\text{AP}^{*}+0.778\text{WS}^{*}-0.018\text{SH}^{*}-0.106\text{RH} ^{*}-0.2\text{PM}^{*}_{2.5}-0.375\text{PM}^{*}_{10}+0.226\text{SO}^{*}_{2}+0. 16\text{NO}^{*}_{2}+0.348\text{CO}^{*}\]  
The absolute values of the coefficients of SO\({}_{2}\), NO\({}_{2}\), and CO in prin1 are the largest of the first three items, which are 0.457, 0.449, and 0.47, respectively, so prin1 combines the factors of SO\({}_{2}\), NO\({}_{2}\), and CO, which is called the composite factor of sulfur and nitrogen carbon oxide pollution, reflecting 37.6% of the information of the original factors. The absolute values of the coefficients of PM\({}_{2.5}\) and PM\({}_{10}\) in prin2 are the two largest, 0.456 and 0.635, respectively. Thus, prin2 combines PM\({}_{10}\) and PM\({}_{2.5}\) air pollutant factors and is called the composite factor of particulate matter pollution, reflecting 19.2% of the information of the original factors. The absolute value of the SH coefficient is the largest in prin3, with a value of 0.668. Thus, prin3 is called the composite factor of sunshine hours, reflecting 15.3% of the information of the original factors. The absolute value of the AP coefficient is 0.83, which is the largest in prin4. Therefore, prin4 is called the air pressure composite factor and reflects 8.8% of the information of the original factor. The largest absolute value of WS coefficient in prin5 is 0.778, called the wind speed composite factor, which reflects 7.7% of the information of the original factor. The data of the nine factors of the 1771 groups of samples in Tables 3 and 4 were substituted into the five principal component expressions, and the principal component scores of each group of samples were calculated using Equation (4) as prin1-prin5, and the output results are shown in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Principal** & **Eigen Value** & **Contribution Rate** &
\begin{tabular}{c} **Cumulative** \\ **Contribution Rate** \\ \end{tabular} \\ \hline
1 & 3.382 & 0.376 & 0.376 \\
2 & 1.727 & 0.192 & 0.568 \\
3 & 1.377 & 0.153 & 0.721 \\
4 & 0.793 & 0.088 & 0.809 \\
5 & 0.694 & 0.077 & 0.886 \\
6 & 0.441 & 0.049 & 0.935 \\
7 & 0.275 & 0.031 & 0.966 \\
8 & 0.215 & 0.024 & 0.989 \\
9 & 0.096 & 0.011 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Eigen values and contribution rates. The first two principal components are extracted from the air pollutant factors, which contribute more significantly to the air quality, and the month-by-month averages of prin1 and prin2 are plotted under the same coordinate system, as in Figure 5.  
As can be seen from Figure 5, the sample time points with higher prin1 scores are concentrated in December to February, indicating that there are more local sulfur and nitrogen carbon oxide pollution emissions in winter, which is closely related to coal-fired heating, increased traffic volume, and higher air pressure and static windy weather, and pollutants are difficult to diffuse.