# Application of Data Mining Techniques to Predict Luminance of Pavement Aggregate
## 4 Analysis of the Research Results  
### Evaluation of the Effectiveness of Selected DM Techniques  
The modeling process began by performing a series of simulations using the algorithms presented in Section 3, namely: C&RT, RF, BT, ANN, and SVM. In the case of ANN and SVM, some additional work was required to find the optimal parameters. In the case of ANN, a series of iterative steps were required to determine the optimal structure of the neural network in terms of the type of activation function and the number of neurons inthe hidden network. On the other hand, in the case of SVM, the parameters of the radial functions C are part of the Kernel function of the SVM method [50]. Qualitative evaluation of DM technique selection was performed using popular regression metrics and is provided in Table 4.  
The selection of the final DM technique required obtaining a minimum MAE or RMSE and a maximum R2 value. It should be kept in mind that the feature for which DM-predictive techniques were used was the luminance coefficient Qd. In the first stage, the dataset containing 1895 valid cases was divided into two subsets:  
* a teaching set containing 70% of randomly selected cases;
* a test set containing 30% of randomly selected cases. Following the stage of constructing a series of DM models, a collection of predicted values of the luminance coefficient Qd was obtained, which are shown collectively in Figure 6.  
Observing the results in Figure 6, it should be noted that the least impressive DM technique, among those used, was SVM. In this case, the obtained model did not allow proper prediction of large and small values of the luminance coefficient Qd, which do not necessarily represent outliers. This is probably due to the fact that the qualitative variables were on a nominal rather than an ordinal scale. Other techniques have shown far greater effectiveness. Nevertheless, observing the influential values occurring (extreme values on the regression line), it can be expected that the BT technique was by far the most effective in relation to the problem in question, which was the effective prediction of the Qd feature. In order to make a final assessment as to the choice of the appropriate technique, the characteristics given in Table 4 were used, while their calculated values are shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **Description** & **Form** \\ \hline R-squared & R2 & \(\left(\frac{\sigma_{yy}}{\sigma_{y}},\sigma_{y^{\prime}}\right)^{2}\) \\ Root mean square error & RMSE & \(\sqrt{\frac{\sum_{i=1}^{N}\left(y_{i}-y_{y_{y_{y}}}\right)^{2}}{N}}\) \\ Mean absolute error & MAE & \(\frac{\sum_{i=1}^{N}\left|y_{i}-y_{y}\right|}{N}\) \\ \hline \hline \end{tabular} \(y_{y}\)—predicted value, \(y_{y}\)—experimental value, \(y_{y}\)—i-th observed value, \(y_{y}\)—mean value, \(\sigma_{y}\)—variance of experimental data, \(\sigma_{y^{\prime}}\)—variance of predicted data, \(\sigma_{y}\sigma_{y^{\prime}}\)—covariance of predicted and experimental data.  
\end{table} 
Table 4: Regression metrics of the DM method. Figure 6: Fit of model results with experimental results. As previously speculated, the Boosted Trees (BT, highlighted) algorithm proved to be the best DM technique for predicting the value of the luminance coefficient Qd of an aggregate. During the construction of the BT model, a learning ratio of 0.1 was used [54], while the ratio for drawing learning samples in successive boosting steps was 0.5, based on the recommendations provided in the paper [55]. Its results were very similar relative to all other DM techniques, with the exception of SVM. The SVM method had by far the highest value of variability expressed by RMSE characteristics. Through this, the MAE value (estimation error) was also very large, at 14.5 mcd m\({}^{-2}\) lx\({}^{-1}\). Such a value of variability in the SVM method excluded the possibility of correct discrimination of aggregates of similar color, for example: quartzite and limestone.