# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 4 Discussion  
When comparing the results obtained in the current study with those from similar studies in the literature, the three different algorithms used in our study stand out. Table 6 presents a comparison of this study and other works from the literature based on the testing R\({}^{2}\) values obtained for predicting results using different algorithms and input parameters. [PERSON] and [PERSON] [27] used artificial neural networks (ANNs) and achieved an R\({}^{2}\) value of 0.885. [PERSON] et al. [36] obtained R\({}^{2}\) values of 0.562 with artificial neural networks, 0.360 with genetic programming, and 0.409 with multiple regression analysis. [PERSON] et al. [37] achieved R\({}^{2}\) values of 0.833 with extreme gradient boosting and 0.818 with random forest methods. [PERSON] et al. [38] reported an R\({}^{2}\) value of 0.860 with random forest and a higher value of 0.890 with a gradient boosting tree, using a smaller number of parameters. Lastly, [PERSON] et al. [39] reported an R\({}^{2}\) value of 0.905 using artificial neural networks.  
In this study, an impressive R\({}^{2}\) value of 0.926 was achieved with the random forest model, while the gradient boosting and AdaBoost models showed R\({}^{2}\) values of 0.930 and 0.921, respectively. Overall, the current study achieves superior results compared to those reported in the literature, particularly when using a comprehensive set of input parameters [\(w\), LL, PL, PI, \(e_{0}\), \(G_{\text{s}}\)], highlighting the potential of the methods used in this study to improve the prediction performance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Used Algorithm** & **Input Parameters** & \begin{tabular}{c} **Testing** \\ **R\({}^{2}\)** \\ \end{tabular} \\ \hline [PERSON] [27] & Artificial Neural Network & [\(w\), \(e_{0}\), LL, PI, \(G_{\text{s}}\), W\({}_{\text{sand, silt, clay}}\)] & 0.885 \\ \hline [PERSON] et al. [36] & \begin{tabular}{c} Artificial Neural Network \\ Genetic Programming \\ Multiple Regression Analysis \\ \end{tabular} & \begin{tabular}{c} [\(\text{P}_{\text{h}}\), \(e_{0}\), \(w\), PI, LL] \\ [\(\text{P}_{\text{h}}\), \(e_{0}\), \(w\), PI, LL, FC] \\ \end{tabular} & 0.562 \\ \hline [PERSON] et al. [37] & \begin{tabular}{c} Random Forest \\ Extreme Gradient Boosting \\ \end{tabular} & \begin{tabular}{c} 0.818 \\ 0.833 \\ \end{tabular} \\ \hline [PERSON] et al. [38] & \begin{tabular}{c} Random Forest \\ Gradient Boosting Tree \\ \end{tabular} & \begin{tabular}{c} 0.860 \\ 0.890 \\ \end{tabular} \\ \hline [PERSON] et al. [39] & Artificial Neural Network & [\(w\), LL, PI] & 0.905 \\ \hline \hline \end{tabular} \begin{tabular}{c} Random Forest \\ Gradient Boosting \\ AdaBoost \\ \end{tabular} & \
\begin{tabular}{c} [\(w\), \(e_{0}\), LL, PL, PI, \(G_{\text{s}}\)] \\ [\(w\), \(e_{0}\), LL, PI, \(G_{\text{s}}\)] \\ [\(w\), AdaBoost \\ \end{tabular} &
\begin{tabular}{c} 0.926 \\ 0.930 \\ 0.921 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of the results of the testing R\({}^{2}\) between this study and previous studies.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Input Combination** & **Training R\({}^{2}\)** & **Testing R\({}^{2}\)** \\ \hline Random Forest & [\(w\), PL, PI, \(e_{0}\)] & 0.970 & 0.928 \\  & [\(w\), PL, PI, \(e_{0}\), \(G_{\text{s}}\)] & 0.970 & 0.926 \\ \hline \multirow{2}{*}{Gradient Boosting} & [PL, LL, \(e_{0}\), \(G_{\text{s}}\)] & 0.916 & 0.932 \\  & [\(w\), PL, LL, PI, \(e_{0}\), \(G_{\text{s}}\)] & 0.925 & 0.930 \\ \hline AdaBoost & [\(w\), PL, LL, PI, \(e_{0}\), \(G_{\text{s}}\)] & 0.847 & 0.921 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The R\({}^{2}\) results obtained from the training and testing of various input combinations.