# Application of Data Mining Techniques to Predict Luminance of Pavement Aggregate
## 4 Analysis of the Research Results
### Validation of the Adopted Boosted Trees Model  
The final validation of the adopted DM model is crucial to verifying the reasoning adopted and the correctness of the rules adopted. Model validation was performed using an additional two validation sets containing drawn aggregate types. Each harvest was subjected to Qd and RL determination by two independent operators and included in its entirety the step of preparing aggregates and performing a series of tests again. Such an action was intended to take into account the effect of randomness due to the human factor, randomness due to the location on the aggregate collection heap, and to confirm the stability of the obtained DM model. Based on previous experiments, it was determined that it would be most appropriate to prepare the samples with surface compaction and supplement the sample level with additional aggregate, caused by the compression of the compaction process (KZ + D based on Table 2). Batches of aggregates with the characteristics listed inTable 6 were drawn for verification analysis. In Table 6, the aggregates selected, along with the grain size, are highlighted in bold font. In the next step, retroreflectometer tests were performed in the same way as when the results were obtained to build the learning and testing set. The accumulated database of results was transferred in order to determine the value of the predicted luminance coefficient Qd according to the set of rules in Figure 7. As a result, using the metrics given in Table 4, the following fits between model and experimental data were obtained (Table 7). The validation process confirmed the stability of the model with regard to the aggregate base available in the Swietokrzyskie vovodeship, Poland. The mean absolute error (MAE) of the residuals was larger by up to 3.5 mcd-m\({}^{-2}\).lx\({}^{-1}\)(1 st validation) than the value obtained by the learning and test sets. Moreover, it is less than half of the recommended maximum Qd result range of 10% of its mean value. Therefore, it can be concluded that results received from the validation set did not differ from the adopted requirements of WT-2/2014 [41], and the error discrepancy was negligible in comparison to the obtained machine learning model. Finally, the values of single readings of the luminance coefficient Qd validation process, along with its prediction, were projected in Figure 12. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Type of Aggregate** & **Grain Size** \\ \hline
1. & **Amphibolite** & **0/2**, 5/8, 8/11 \\
2. & **Basalt** & 2/5, 5/8, 8/11, **16/22** \\
3. & **Gabbro** & **2/5**, 5/8, 8/11 \\
4. & **Granite** & 2/8, **8/16**, 16/22 \\
5. & Quartzite & 0/2, 2/5, 5/8, 8/11, 8/16, \\
6. & **Melaphyre** & 0/2, 2/5, **5/8**, 8/11, 8/16, \\
7. & **Limestone** & 0/2, 2/8, 4/11, **5/11**, 5/8, 8/11, 8/16, 16/22 \\ \hline \end{tabular}
\end{table} 
Table 6: Selection of aggregates for the validation stage. \begin{table}
\begin{tabular}{c c c c} \hline
**DM Method** & **MAE** & **RMSE** & **R2** \\ \hline
**Boosted trees** & & & \\
**(teaching and testing)** & & & \\
1 st validation & 7.8 & 76.1 & 0.76 \\
2 nd validation & 5.7 & 53.2 & 0.85 \\ \hline \end{tabular}
\end{table} 
Table 7: Summary of regression metrics of quality of fit of validation stage of Qd [mcd-m\({}^{-2}\).lx\({}^{-1}\)]. [PERSON] and red colors indicate the set of validation results. According to the results in Table 7, the \"2 nd validation\" set was characterized by a slightly higher dispersion of results than the \"1 st validation\" set. Nevertheless, the vast majority of results did not deviate from the base set (blue color), on the basis of which the rules of the random tree model were built. Therefore, the efficiency of the BT model built for Qd prediction was satisfactory, and the prediction results were stable. However, obtaining an adequate prediction using BT rules requires the use of a popular retroreflectometer with the ability to determine the RL coefficient.