# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 3 Results
Figure 8: Testing results of the gradient boosting regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. Figure 7: Training results of the gradient boosting regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. We tested all combinations of the six inputs in our dataset one by one for the random forest regressor, gradient boosting regressor, and AdaBoost regressor algorithms. The combinations we tried, totaling 63 all in all, were as follows: single-input combinations ([\(w\)], [PL], [LL], etc. ), two-input combinations ([\(w\), PL], [\(w\), LL], etc. ), three-input combinations ([\(w\), PL, LL], etc. ), four-input combinations ([\(w\), PL, LL, PI], etc. ), five-input combinations ([\(w\), PL, LL, PI, \(e_{0}\)], etc. ), and six-input combinations ([\(w\), PL, LL, PI, \(e_{0}\), \(G_{8}\)]). Ignoring a few combinations that had very small differences of 0.002, the six-input combination, which included all the inputs in the dataset, showed the most successful results for all three algorithms. Table 5 displays only the highest training and testing R\({}^{2}\) results obtained with different input combinations of the algorithms used in this study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Parameter Combination** & **Training R\({}^{2}\)** & **Testing R\({}^{2}\)** \\ \hline \multirow{3}{*}{Random Forest} & First selection (100, 1.0, 20) & 0.9708 & 0.9264 \\  & Second selection (100, 1.0, 30) & 0.9706 & 0.9265 \\  & Third selection (100, 1.0, 50) & 0.9706 & 0.9265 \\ \hline \multirow{3}{*}{Gradient Boosting} & First selection (\(10^{-1}\), squared) & 0.9250 & 0.9300 \\  & Second selection (\(10^{-1}\), Huber) & 0.9040 & 0.9220 \\  & Third selection (\(10^{-1}\), absolute) & 0.8510 & 0.8920 \\ \hline \multirow{3}{*}{ AdaBoost} & First selection (200, 1.0, square) & 0.8470 & 0.9217 \\  & Second selection (100, 1.0, square) & 0.8468 & 0.9210 \\ \cline{1-1}  & Third selection (10, 1.0, exponential) & 0.8468 & 0.9100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The R\({}^{2}\) results obtained from the training and testing of various parameter combinations. Figure 10: Testing results of the AdaBoost regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. Figure 9: Training results of the AdaBoost regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. The random forest regressor with the six-input combination ([\(w\), PL, LL, PI, \(e_{0}\), \(G_{\text{s}}\)]) achieved impressive R\({}^{2}\) scores of 0.970 for training and 0.926 for testing. The gradient boosting regressor performed slightly better in testing with a four-input combination ([PL, LL, \(e_{0}\), \(G_{\text{s}}\)]), with a training R\({}^{2}\) score of 0.916 and testing R\({}^{2}\) score of 0.932, while the six-input combination yielded a marginally higher training R\({}^{2}\) value of 0.925 but a slightly lower testing R\({}^{2}\) value of 0.930. The AdaBoost regressor lagged slightly behind when using the six-input combination, with training and testing R\({}^{2}\) scores of 0.847 and 0.921, respectively.