# 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 coarser the aggregates, the more luminance coefficient values begin to diverge. The median luminance coefficient of all results was about 80 mcd m\({}^{-2}\) lx\({}^{-1}\), which was higher than the Polish requirement to use aggregates for pavement brightening with Qd \(>\) 60 mcd m\({}^{-2}\) lx\({}^{-1}\) as per WT-2/2014 [41]. In terms of Polish recommendations, the recommended fractions for luminance coefficient testing are 4/8, 5/8 or 8/11. Nevertheless, numerous other aggregate fractions were used for the purpose of teaching the model. It should be noted that 5/8 and 8/11 fractions in the models yielded very similar values of the median luminance coefficient of the tested aggregates (Figure 9). Therefore, the luminance coefficient test should be performed for coarse aggregate \(>\) 4 mm, which confirms the validity of the proposed fractions in the adopted recommendations, although the tests performed for the 8/11 aggregate fraction were characterized by a larger interquartile range (Q3-Q1). In addition, outliers were observed representing the Qd results of aggregate with 0/2 grain size in all aggregate cases. The Qd value for this fraction obtained a much higher value than the other cases of a given aggregate. Therefore, this type of fraction should not be used as representative, whereas its presence in the tests was intended to increase the effectiveness of the BT model rules. A summary of the distribution of the luminance coefficient is shown in Figure 10.  
Figure 10: Distribution of Qd,pred (predicted) and RL (box: 25-75%; whisker: non-outlier). Figure 9: Plot of Qd variation against aggregate type and grain size. A preliminary comparison of both luminance coefficients (Qd,pred and RL) in Figure 10 suggests that the most suitable aggregates (median) for pavement brightening are granite (Qd = 99 mcd m\({}^{-2}\) lx\({}^{-1}\)), limestone (Qd = 85 mcd m\({}^{-2}\) lx\({}^{-1}\)), and quartzite (Qd = 86 mcd m\({}^{-2}\) lx\({}^{-1}\)). All offer definitely greater luminance coefficient values than the recommended baseline, i.e., 60 mcd m\({}^{-2}\) lx\({}^{-1}\)[41]. Aggregates that yielded approximately borderline results are amphibolite (Qd = 61 mcd m\({}^{-2}\) lx\({}^{-1}\)) and gabbro (Qd = 59 mcd m\({}^{-2}\) lx\({}^{-1}\)). Therefore, they can be used conditionally as alternative pavement-brightening solutions. The others do not achieve the intended pavement-brightening effect. An interesting issue is the value of the RL coefficient, which does not fully correlate with the values of the predicted Qd,pred. Visibility at night probably depends on the presence of certain minerals in the aggregate, which allow significant luminance of the aggregate when illuminated by vehicle lighting. This is a similar case to a situation when horizontal markings containing glass beads in the paint are evaluated. Typically, the introduction of beads increases nighttime visibility (RL). However, it significantly reduces the Qd value, which reflects the perception of pavement illuminated by sunlight, i.e., illumination incident at a different angle than that of vehicle lighting. Quartzite and granite aggregates, despite their high Qd,pred values, did not achieve the same range of RL as limestone aggregate. Therefore, it can be concluded that the best solution for brightening pavement is to use common limestone aggregate. Very relevant to a given analysis are the results of the interaction between the predicted value of the luminance coefficient Qd,pred and the accompanying RL value, as shown in Figure 11.  
Figure 11 is essentially a collection of histograms. It allows the determination of the local peaks (frequencies) of the luminance coefficient Qd,pred. The quantitative nighttime visibility parameter RL was used as an accompanying variable. It should be clearly emphasized that the use of a single central measure to describe a set such as the mean or median does not allow an exhaustive characterization of the distribution of the luminance coefficient (as in Figure 10).