# Random Forests and Cubist Algorithms for Predicting Shear Strengths of Rockfill Materials
## 3 Results and Discussion
### Results of Independent Test Set  
To validate the predictive models based on the predicted and measured (real) values, 32 testing samples were validated by the optimized random forests and Cubist models. Figure 6 and Table 2 illustrate the regression results. Figure 6 shows the actual vs predicted the shear strength of RFM by linear regression, random forests and the Cubist algorithm using test data. Figure 6 suggests that all predicted values by random forests and the Cubist method lie within \(\pm\) 25% error from the line of  
Figure 4: Fivefold cross-validated RMSE profiles for determining the optimal tuning parameters: (a) Random forests model, and (b) Cubist model.  
Figure 5: Comparison of the performance of the four algorithms with the MAE, RMSE and R\({}^{2}\) metrics.  
perfect agreement. In Figure 6, the RMSE, R\({}^{2}\) and MAE between the observed values and predicted values of the random forests model were 0.1133, 0.9548 and 0.0665, respectively, for the test data. The RMSE, R\({}^{2}\) and MAE for the predicted values using the Cubist method were 0.0959, 0.9697 and 0.0671, respectively, for the test data. Additionally, the RMSE, R\({}^{2}\) and MAE of the predicted values using the conventional multiple linear regression method [56] were 0.1361, 0.9345 and 0.0888, respectively, for the test data. The RMSE, R\({}^{2}\) and MAE of the predicted values using the ANN method [20] were 0.1361, 0.9345 and 0.0888, respectively, for the test data. The performance has been improved by random forests and Cubist modeling approaches compared with the conventional multiple linear regression and artificial neural network in terms of R\({}^{2}\), RMSE and MAE values (Table 2). In particular, the Cubist model yielded the best result in the section of testing datasets. As a strong tool for modeling the rule-based models, the Cubist model is able to balance the relationship between the predictive accuracy and the requirements of intelligibility.  
Although direct measurement of the shear strengths of rockfill materials is a reliable method, efforts should be made to overcome the complexities of the experiment, especially the difficulties of obtaining rock samples from field sites. Different testing procedures for determining the shear strengths of rockfill materials may yield substantial differences in the results, and most rock testing laboratories are not equipped to perform tests for determining the shear strengths of rockfill materials. A possible substitutional method is to study the shear behaviors of rockfill materials using the relationships between the shear parameters and the physicochemical properties of rockfill materials and develop a prediction method for evaluating the shear strengths of rockfill materials via machine learning approaches. For the given training dataset and regression target, both Cubist regression and random forests show effective prediction ability with the specification of a few tunable model parameters as previously mentioned. As advanced data-driven tools, these two supervised machine learning techniques have the potential for learning the complex interrelationships between explanatory data variables and the target property.