# Random Forests and Cubist Algorithms for Predicting Shear Strengths of Rockfill Materials
## 3 Results and Discussion
### Variable Importance and Interpretation  
The importance of influencing variables can be individually evaluated by the feature importance to aid in the interpretation of previous results based on the decrease of Gini impurity when a variable  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **RMSE** & **MAE** \\ \hline Linear regression & 0.9345 & 0.1361 & 0.0888 \\ Cubist & 0.9645 & 0.0975 & 0.0644 \\ Artificial neural network & 0.9386 & 0.1320 & 0.0841 \\ Random forest & 0.9523 & 0.1282 & 0.0860 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The performance of different prediction models for test data.  
Figure 6: Error of the shear strength of RFM for the testing set.  
is chosen to split a node [32]. The sensitivity analysis of the indicators is conducted to determine the degree of contribution of each variant indicator among all estimation cases. The Cubist model in this database employed the 13 parameters of D\({}_{10}\), D\({}_{30}\), D\({}_{60}\), D\({}_{90}\), Cc, Cu, Gm, Fm, R, UCSmin, UCSmax, \(\gamma\) and Ns. The results for the Cubist model are given in Figure 7a, which demonstrates the relative variable importance for the final Cubist model. Among all indicators in the final Cubist model for the prediction of the shear strength of RFM with the given dataset, Ns and D\({}_{60}\) are the two most influential parameters, followed by the indicators D\({}_{10}\), Cu, Fm, D\({}_{90}\), Gm, D\({}_{30}\), Cc, \(\gamma\), R, UCSmin and UCSmax.  
Similarly, the random forests model in this database used 13 previously mentioned parameters. Compared with other indicators for the prediction of the shear strength of RFM, Ns and D\({}_{10}\) are the two most influential parameters, followed by the indicators D\({}_{90}\), Gm, D\({}_{30}\), Fm, D\({}_{60}\), Cu, \(\gamma\), R, Cc, UCSmin and UCSmax, as depicted in Figure 7b. Interestingly, the min UCS and max UCS indicators did not contribute to the performance of the proposed models. These results are also consistent with the correlation matrix of the variables that have the highest coefficients for these variables. The findings demonstrated that the Cubist and random forests predictors are more sensitive to the indicators of normal stress and material gradation properties but are not sensitive to min UCS and max UCS. This result implies significant guidance for exploring the characteristics of the shear strength of RFM. Similar research of sensitivity analyses on this topic was also implemented by [PERSON] [20], who reported the rankings of the following input parameters: normal stress, minimum particle strength, dry unit weight, 10% passing sieve size, the coefficient of curvature of the particle size distribution, and the coefficient of uniformity of the particle size distribution in decreasing order of significance, which shows agreement with the previously mentioned results. Note that more data about the in-situ shear strength of RFM need to be supplemented to yield more reliable importance scores of random forests and Cubist models for influential variables in future research.