## 4 Results  
### Support Vector Machine (SVM)  
In order to derive an optimal SVM model, multiple parameters were adjusted, and the resulting model with the most favorable performance is delineated in this section. Table 4 presents the specifications of the best support vector machine (SVM) model derived through parameter tuning. The model was constructed using the sequential minimal optimization (SMO) algorithm, with a penalty parameter of \(C=2\), and a tolerance value of 0.001. The epsilon parameter, which controls the width of the margin, was set to 0.5. The input data was pre-processed using standardization, to ensure that each feature had a mean of zero and a standard deviation of one. The kernel function used in this model was the radial basis function (RBF), which is a popular kernel function for SVMs due to its flexibility in modeling complex, nonlinear relationships between input variables. The gamma parameter of the RBF kernel was set to 0.5, which controls the smoothness of the decision boundary. A lower value of gamma, results in a smoother decision boundary, while a higher value of gamma, leads to a more complex boundary, that can overfit the data. Overall, these specifications provide a well-performing SVM model, that can accurately classify data while avoiding overfitting. These parameters can be used as a starting point for future SVM modeling tasks or as a benchmark for comparing the performance of other SVM models. The predicted values of CBR against the values obtained from the tests in the laboratory for the training and testing database, are shown in Figure 7. The results show that the SVM model has been able to predict the CBR values with a good accuracy. Table 5 presents the performance metrics of the SVM used to predict the California bearing ratio (CBR) values for mixtures of alum sludge and soil. Both training and testing datasets were used to evaluate the performance of the SVM model. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{3}{c}{**SMO Parameters**} & \multicolumn{3}{c}{**Kernel Parameters**} \\ \hline \(C\) & Tolerance & Epsilon & Pre-processing & Type of Kernel & Gamma \\
2 & 0.001 & 0.5 & Standardization & Radial basis function (RBF) & 0.5 \\ \hline \end{tabular}
\end{table} 
Table 4: The specifications of the best performing SVM. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance Metrics** & **Training Database** & **Testing Database** \\ \hline MAE & 0.497 & 0.512 \\ MSE & 0.409 & 0.357 \\ RMSE & 0.640 & 0.598 \\ MSLE & 0.017 & 0.011 \\ RMSLE & 0.129 & 0.103 \\ R\({}^{2}\) & 0.978 & 0.939 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of SVM predictions of CBR for mixtures of alum sludge and soil. The first performance metric is the mean absolute error (MAE), which measures the average absolute difference between the predicted and actual CBR values. In the training and testing sets, the values are 0.497 and 0.512, respectively, indicating that the model has an average error of approximately 0.5. A second performance metric is the mean squared error (MSE), which measures the average squared difference between the predicted and actual CBR values. The training and testing sets have values of 0.409 and 0.357, respectively, indicating that the model has a relatively low overall error in predicting the CBR values. The third performance metric, is the root mean squared error (RMSE), which is the square root of the mean square error (MSE). The training and testing sets have values of 0.640 and 0.598, respectively, indicating that the model has a relatively low overall error in predicting the CBR values. The fourth performance metric is the mean squared log error (MSLE). The MSLE measures the difference between the logarithm of the predicted CBR values and the logarithm of the actual CBR values. For the training and testing sets, the values are 0.017 and 0.011, respectively, indicating that the model has a relatively low overall error when predicting the CBR values.