## 4 Results and Discussion
### Comparison of Integrated ML Algorithms  
As discussed above, six ML algorithms were employed to examine their predictive effects in the dataset. Figure 7 shows the predictive performance of the six ML algorithms in terms of the most commonly used statistical measures: MSE and R\({}^{2}\). It can be observed that BPNN, DT, and SVM have better performance than other modules. Besides, DT outperformed BPNN and SVM with a marginally smaller MSE and slightly higher R\({}^{2}\). The worst-performing algorithm was LR with the highest MSE of 6.1202 and the lowest R\({}^{2}\) of 0.3089. This indicates that this baseline algorithm is not suitable for modeling the UCS data.  
The differences between the predicted and actual values in the testing dataset can be compared using the boxplot (see Figure 8). A boxplot is convenient to visually display the distribution of the data through their quartiles [53]. It can be seen that DT was grouped the most tightly (with a comparatively short boxplot), and was slightly better than BPNN and SVM, although no outliers were observed in SVM. This indicates the overall UCS values of the composites were predicted accurately by these three  
Figure 6: MSE versus iteration for five individual ML algorithms.  
Figure 7: Predicted and actual UCS in the test dataset: (**a**) BPNN, (**b**) SVM, (**c**) DT, (**d**) RF, (**e**) KNN, (**f**) LR.  
algorithms. As for RF, KNN, and LR, these boxplots are comparatively tall with larger interquartile ranges and more outliers, indicating that the predicted UCS values were more scattered. LR was the worst-performing algorithm in terms of the highest median and largest interquartile range.  
The realistic characteristics of these ML algorithms can be graphically indicated by a Taylor diagram [54]. The Taylor diagram shown in Figure 9 provides a summary of the skill with which the six ML algorithms simulate the relationship between the predicted and observed UCS. The distance between each ML algorithm and the point labeled \"measured\" is a measure of how realistically each algorithm reproduces the measured values. It is clear that DT, SVM, and BPNN lie nearest the point marked \"measured\" with comparatively higher R\({}^{2}\) and lower RMSE, demonstrating that the three algorithms agree well with the actual values. LR has a low pattern correlation, while KNN has larger variations than the actual values. It should be noted that although RF has about the same correlation coefficient as SVM, DT and BP, the standard deviation of RF is much larger, resulting in a larger RMSE.  
Figure 8: Box plot of the results comparison of proposed ML algorithms.  
Figure 9: Taylor diagram for presenting the predictive effect of six models.  
To compare these ML algorithms more comprehensively, some other statistics including mean absolute error (MAE), mean absolute percentage error (MAPE), minimum iteration, and time cost were also introduced in this study. To visualize data with so many variables, a radar chart is a good choice. The radar chart is composed of a series of equi-angular spokes arranged radially from the center, with each spoke standing for one statistical measure. The spoke length is proportional to the normalized magnitude of the measure between 0 (worst) to 1.0 (best) [55], and hence, a better model encloses a worse model. It is easily seen from Figure 10 that DT, SVM, and BPNN performed the best overall, and enclosed RF, KNN, and LR, although SVM performed slightly worse in terms of iteration times, indicating that SVM cost more time and effort during modeling. Among the models with poorer performance, LR was nearly enclosed by KNN due to lower scores for several variables including MSE, MAE, R, R\({}^{2}\), and difference median. RF performed better in all the statistics except minimum integration, but many scores were not high enough to represent a good prediction model such as MSE, MAE, MAPE, and difference median.