# Prediction of Ground Subsidence Risk in Urban Centers Using Underground Characteristics Information
## 3 Analysis of Data Correlations  
The correlation between the input and output data included in the dataset was examined to develop an optimal ground subsidence risk prediction model. Correlation analysis is a method used to determine the existence of a linear relationship between the independent (input data) and dependent variables (output data), as well as to assess the strength of the relationship between the variables [18]. In this study, significant factors between the two variables were selected through Pearson correlation analysis and were used in model training. The correlation between two variables was calculated using Equation (1). A larger absolute value of the correlation coefficient corresponds to a stronger correlation between the two variables [19]. \[Corr(X,Y)=\rho(X,Y)=\frac{Cov(X,Y)}{\sigma_{x}\sigma_{y}}, \tag{1}\]  
where \(\sigma_{x}\wedge\sigma_{y}\) denote the standard deviations of the variables. Ground subsidence results from a complex interplay between various factors, and identifying a single variable with a high correlation to ground subsidence is difficult. Therefore, statistically significant factors related to ground subsidence risk were selected from the input data and used in the training dataset. The degree of statistical significance was examined using a test statistic (Equation (2)) to evaluate the correlation within the data [20]:  
\[t=r\sqrt{\frac{n-2}{1-r^{2}}}, \tag{2}\]  
where r denotes the sample correlation coefficient, and n is the sample size. The correlation between the ground subsidence risk and extracted representative values of the input data (density, permeability, thickness, height) was analyzed using the preprocessed dataset for a total of 12 cases, and the results are presented in Table 4. Y and DTR in Table 4 denote the years of use and pipe diameter, respectively. 5Y and 10Y denote 5 and 10 years of use, respectively; 5-50 represents the range of the data. 50 DTR and 100 DTR denote units corresponding to pipe diameters of 50 mm and 100 mm, respectively. 50-1000 indicates the range of pipe diameters. A \(p\)-value of less than or equal to 0.05 is deemed statistically significant, and the corresponding data were used as input data [21]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model No.** & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} \\ \hline
**Factor** & **Corr** & \(p\)**-Value** & **Corr** & \(p\)**-Value** & **Corr** & \(p\)**-Value** \\ \hline
5Y\_5 & 0.122 & 0.000 & 0.125 & 0.000 & 0.127 & 0.000 \\
5Y\_10 & 0.064 & 0.000 & 0.065 & 0.004 & 0.070 & 0.002 \\
5Y\_15 & 0.212 & 0.000 & 0.205 & 0.000 & 0.217 & 0.000 \\
5Y\_20 & 0.337 & 0.000 & 0.328 & 0.000 & 0.329 & 0.000 \\
5Y\_25 & 0.51 & 0.000 & 0.516 & 0.000 & 0.526 & 0.000 \\
5Y\_30 & 0.472 & 0.000 & 0.477 & 0.000 & 0.470 & 0.000 \\
5Y\_35 & 0.414 & 0.000 & 0.405 & 0.000 & 0.410 & 0.000 \\
5Y\_40 & 0.478 & 0.000 & 0.483 & 0.000 & 0.490 & 0.000 \\
5Y\_45 & 0.509 & 0.000 & 0.527 & 0.000 & 0.537 & 0.000 \\
5Y\_50 & 0.426 & 0.000 & 0.442 & 0.000 & 0.449 & 0.000 \\
50 DTR\_50 & 0.331 & 0.000 & 0.328 & 0.000 & 0.337 & 0.000 \\
50 DTR\_100 & 0.455 & 0.000 & 0.461 & 0.000 & 0.471 & 0.000 \\
50 DTR\_150 & 0.474 & 0.000 & 0.478 & 0.000 & 0.480 & 0.000 \\
50 DTR\_200 & 0.523 & 0.000 & 0.521 & 0.000 & 0.526 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the correlation analysis of influencing factors.