# Construction of Air Quality Level Prediction Model Based on STEPDISC-PCA-BP
## 3 Results and Discussion
### PCA Method to Reduce the Factors Dimension  
To reduce the number of input nodes of the BP neural network, principal component analysis was performed based on the discriminant significant factors in Table 3 to further reduce the data dimensionality. The pearson correlation coefficients of the 9 factors in Table 3 were calculated to verify the existence of correlation between the factors, and the calculation results are shown in Table 4.  
As can be seen from Table 4, the correlation coefficient between PM\({}_{2.5}\) and PM\({}_{10}\) is the largest, 0.7765, which is moderately correlated. The main sources of PM\({}_{2.5}\) are both primary particulate matter directly emitted from coal combustion, fuel oil motor vehicle exhaust, ground dust, and restaurant fumes, and secondary fine particles generated by chemical reactions of nitrogen oxides and volatile organic compounds in the air. About 70% of PM\({}_{10}\) is PM\({}_{2.5}\), and as PM\({}_{10}\) emissions increase, PM\({}_{2.5}\) concentrations show an increasing trend. NO\({}_{2}\), SO\({}_{2}\), and CO have the next highest correlation coefficients, 0.7476 and 0.7236, respectively. CO is contained in the flue gas of SO\({}_{2}\) generated by the use of coal, natural gas, and other fuels due to insufficient combustion, and the three air pollutants have the same increasing or decreasing relationship [18; 19; 20]. SH and RH are negatively correlated with a correlation coefficient of \(-0.5112\), with a decrease in sunshine hours bringing an increase in relative humidity. In summary, there are obvious correlations between meteorological factors and between some air pollutant factors, which have synergistic effects on the superiority and inferiority of air quality. Principal component analysis is considered to extract new mutually independent principal components to explain as much information of \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **AP** & **WS** & **SH** & **RH** & **PM\({}_{2.5}\)** & **PM\({}_{10}\)** & **SO\({}_{2}\)** & **NO\({}_{2}\)** & **CO** \\ \hline AP & \(1\) & & & & & & & & \\ WS & \(-0.2644\) & \(1\) & & & & & & & \\ SH & \(-0.2047\) & \(-0.0193\) & \(1\) & & & & & & \\ RH & \(0.1595\) & \(-0.1473\) & \(-0.5112\) & \(1\) & & & & & \\ PM\({}_{2.5}\) & \(0.0038\) & \(-0.0191\) & \(-0.2614\) & \(0.1867\) & \(1\) & & & & \\ PM\({}_{10}\) & \(-0.1162\) & \(0.1787\) & \(-0.1207\) & \(-0.00974\) & \(0.7765\) & \(1\) & & & \\ SO\({}_{2}\) & \(0.3566\) & \(-0.3195\) & \(-0.2085\) & \(0.1481\) & \(0.4875\) & \(0.1332\) & \(1\) & & \\ NO\({}_{2}\) & \(0.2297\) & \(-0.3680\) & \(-0.0944\) & \(0.1391\) & \(0.5049\) & \(0.1350\) & \(0.6993\) & \(1\) & \\ CO & \(0.2309\) & \(-0.2254\) & \(-0.2404\) & \(0.2712\) & \(0.5511\) & \(0.1693\) & \(0.7236\) & \(0.7476\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson correlation coefficient matrix for discriminant significant factors. Figure 4: Annual average of AQI for 2015–2019. the original factors as possible. The results of calculating the eigenvalues and contribution rates of the correlation coefficient matrix of Table 4 are shown in Table 5.  
Table 5 is arranged in descending order according to the eigen values. The contribution rate of the top 5 are 37.6%, 19.2%, 15.3%, 8.8%, and 7.7%, respectively, covering a total of 88.6% of the information from nine factors. At a contribution threshold of 85%, the top 5 principal components were selected.