# Prediction of Soil Compaction Parameters Using Machine Learning Models
## 2 Materials and Methods
### Statistical Analysis of Database  
Pearson's correlation coefficient is a common method to measure the degree of linear correlation between parameters. In machine learning, Pearson's correlation coefficient can discover the linear relationship between features by calculating the correlation coefficient between different features, and by avoiding redundant feature information input into the model. In addition, Pearson's correlation coefficient, by calculating the correlation coefficient between each feature and the target variable, allows for the selection of features that are highly correlated with the target variable for constructing machine learning models. This helps us to reduce the feature dimension and improve the explanatory ability and generalization performance of the model.  
Figure 1 illustrates the distribution of the parameter densities and the Pearson correlation coefficients between the parameters, with the Pearson correlation coefficients denoted by r. The \(r\) within \(\pm\)0.81 to \(\pm\)1.0, \(\pm\)0.61 to \(\pm\)0.80, \(\pm\)0.41 to \(\pm\)0.60, \(\pm\)0.21 to \(\pm\)0.40, and \(\pm\)0.0 to \(\pm\)0.20 represents very strong, strong, moderate, weak, and irrelevant, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Statistics** & \begin{tabular}{c} **Fine Content** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Sand Content** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Specific** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Liquid Limit** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Plastic Limit** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Optimum Moisture** \\ **Content (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Maximum Dry** \\ **Density (\text@kN/m\({}^{3}\))** \\ \end{tabular} \\ \hline Mean & 53.55 & 37.27 & 2.7 & 41.91 & 23.01 & 17.55 & 17.12 \\ Standard & 17.05 & 13.87 & 0.06 & 12.4 & 5.93 & 4.82 & 1.42 \\ Minimum & 13 & 2 & 2.58 & 23.1 & 13.68 & 7.6 & 12.6 \\ Maximum & 98 & 80 & 2.85 & 115 & 45.3 & 36.8 & 20.51 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics of soil database.  
Figure 1: Detail of Pearson’s correlation coefficient/matrix of soil database. _FC_ fine content; \(S\) sand content; _SG_ specific gravity; _LL_ liquid limit; _PL_ plastic limit; _OMC_ optimum moisture content; _MDD_ maximum dry density; \(r\) Pearson correlation coefficient; _R_\({}^{2}\) coefficient of determination.  
As shown in Figure 1, FC has a strong correlation with S (\(-\)0.7189) and MDD (\(-\)0.6151), and a moderate correlation with LL (0.4899) and OMC (0.5703). S has medium correlation with LL (\(-\)0.4442), MDD (0.4414), and OMC (\(-\)0.3997). There was no complex covariance between FC and LL, PL, OMC, and MDD. Therefore, FC, S, LL, and PL can be used as input characteristics to predict OMC and MDD.  
SGI is largely independent of the other parameters. This shows that SG, as an input feature, contributes to a very small extent to predicting OMC and MDD. In addition, LL was strongly correlated with PL (0.7966), OMC (0.7990), and MDD (\(-\)0.7520). PL has a very strong correlation with OMC (0.8497) and MDD (\(-\)0.7901) and a weak correlation with FC (0.3869) and S (\(-\)0.2880). The results indicate that LL is multicollinear with PI and OMC.