# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 3 Results  
Machine learning algorithms have variables called parameters, similar to mathematical equations. Just as changing the value of a variable in a mathematical equation alters the result, the same applies to machine learning algorithms. Therefore, each algorithm used in  
Figure 4: Flowchart of all research and analysis procedures. the study was trained and evaluated with the parameters LL, \(w\), PL, PI, \(G_{s}\), and \(e_{0}\) and the compression index (C\({}_{c}\)) using the same training and testing sets. One of purposes of this study was to identify the parameter values that yielded the best outcomes by assigning different values to three parameters of the random forest regressor algorithm: the number of estimators, the number of maximum features, and the maximum depth of the tree. For the parameter of the number of estimators, which indicates the number of trees in the random forest, we used integer values of 10, 50, 100, 200, and 400, respectively. For the parameter of the number of maximum features, which determines the number of features to consider when seeking the best split, we used the options no change (1.0), square root, and logarithmic change. For the maximum depth of the tree parameter, we used integer values of 10, 20, 30, 40, and 50, respectively. Figures 5 and 6 show the training and testing outcomes with blue circle symbols of the best parameter search for the random forest regressor algorithm. The optimal training R\({}^{2}\) value of 0.970 and testing R\({}^{2}\) value of 0.926 for the random forest regressor were obtained with the parameters number of estimators = 100, number of maximum features = 1.0, and maximum depth = 20. We aimed to identify the optimal values by experimenting with different values for the loss and learning rate parameters of the gradient boosting regressor algorithm. The learning rate parameter was set to multiples of 10 between \(~{}10^{-1}\) and \(10^{-8}\). For the loss function parameter, we employed loss functions including the squared error, absolute error, Huber loss, and quantile. Figures 7 and 8 display the training and testing outcomes with blue circle symbols from the optimal parameter search for the gradient boosting regressor algorithm. The highest training R\({}^{2}\) of 0.925 and the highest testing R\({}^{2}\) of 0.930 for the  
Figure 5: Training results of the random forest regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. Figure 6: Testing results of the random forest regressor parameter search: (**a**) the most successful selection, (**b**) the second most successful selection, and (**c**) the third most successful selection. gradient boosting regressor were achieved with the parameters set to a learning rate \(10^{-1}\) and using a squared error loss function. Experiments were conducted with various values for three parameters of the AdaBoost regressor algorithm--the learning rate, loss function, and number of estimators--to achieve the optimal performance. The learning rate parameter was adjusted to 1.0, 0, and multiples of 10 between \(10^{-1}\) and \(10^{-8}\). We set the parameter of the number of estimators to integer values of 10, 50, 100, 200, and 400. For the loss function parameter, we applied linear, square, and exponential loss functions. Figures 9 and 10 present the training and testing results with bulge circle symbols obtained during the optimal parameter search for the AdaBoost regressor algorithm. The AdaBoost regressor achieved an optimal training R\({}^{2}\) value of 0.847 and testing R\({}^{2}\) value of 0.921 with the following parameters: 200 estimators, a learning rate of 1.0, and a square loss function. Table 4 displays the training and testing R\({}^{2}\) results for the top three selections, which had the highest values, obtained using different parameter combinations with the algorithms used in this study.