# Application of Data Mining Techniques to Predict Luminance of Pavement Aggregate
## 3 DM Evaluation
### Analysis of the Test Set and Its Preprocessing (Data Preprocessing)  
The process of identifying the best data mining technique required performing a series of pre-estimation analyses according to the diagram in Figure 3. Their primary goal was to recognize the structure of the data contained in Table 1. It should be noted that the case selection of this set of aggregates was random. The analyzed samples were subjected to an assessment of the presence of outliers and redundancy resulting from the mutual correlation of the samples. Data mining techniques are not as conservative as when using a multiple regression model; nonetheless, certain steps should be taken to improve the quality of the input set [44]. For the qualitative variables (measurement conditions, grain size, and aggregate origin), Cramer's V method for correlation assessment was used. However, for quantitative features (Qd and RL), the traditional correlation coefficient was used. The value of 0.9 was assumed as a threshold value for both the correlation coefficients r and Cramer's V, which was intended to indicate an extremely high correlation  
Figure 4: Algorithm of data analysis using DM techniques to predict luminance coefficient Qd. between predictors. Quantitative as well as qualitative variables were used in the analysis. Quantitative features represented parameters obtained during direct measurement using a reflectometer, whereas the qualitative features were related to the properties of the aggregate and the test conditions. A summary of the input data is presented in Table 2.  
The distribution of the two quantitative variables (Qd and RL) used to build the DM model is presented in Figure 5.  
It should be noted (Figure 5) that the largest number of cases relative to the Qd feature were in the range of two main intervals of results: the first is \(60\div 70\) mcd-m\({}^{-2}\).lx\({}^{-1}\), and the next is \(90\div 110\) mcd-m\({}^{-2}\).lx\({}^{-1}\). In contrast, the value of the R\({}_{\rm L}\) coefficient was in the range of \(40\div 60\) mcd-m\({}^{-2}\).lx\({}^{-1}\). The input factors studied were also evaluated for outliers. For quantitative variables, a homogeneous interval of <Q1-1.5 IRQ; Q3 + 1.5 IRQ> was used. As a result, only 2% outliers were detected for the R\({}_{\rm L}\) feature. With regard to quality characteristics, grain size--5.3% and test conditions--3.2%. No outliers were detected in the set of other features. Such a low percentage of outliers was indicative of a balanced set; the structure and representativeness for the use of machine learning aimed at proper prediction of aggregate luminance Qd. A summary of basic statistical characteristics is presented in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Quantitative Variable** \\ \hline Qd, mcd\(\cdot\)m\({}^{-2}\).lx\({}^{-1}\) & Luminance coefficient under diffused illumination \\ RL, mcd\(\cdot\)m\({}^{-2}\).lx\({}^{-1}\) & Surface reflectance coefficient \\ \hline  & **Qualitative variable** \\ \hline Petrography & 7 types of aggregates (Table 1) \\ Grain size & (Table 1) \\  & Three classes: \\  & Uncompacted aggregate (KBZ) \\ Test conditions & Compacted aggregate (KZ) \\  & compacted aggregate with filling and leveling of the sample \\  & surface (KZ + D) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of input variables. Figure 5: Distribution of Qd and RL of tested aggregates: (**a**) histogram; (**b**) box and whisker plot. The result of the high positive kurtosis of the RL feature is noteworthy. Its value suggests a clustering of its values around a central value much greater than that of the Qd feature. In addition, its results clustered around the central value with a lower standard deviation compared to the Qd feature. Road pavements typically achieve Qd values in the range of 55 to 90 \(\mathrm{mcd\cdot m^{-2}.lx^{-1}}\) depending on the type of pavement and the color of the aggregate [13].