# Predicting Putting Development Using Machine Learning Methods Based on RIOCHTrack Data
## 2 Methodology
### Preprocessing  
The elimination of outliers within the dataset is crucial for maintaining the integrity and reliability of the data. The popular approaches for outlier detection include probabilistic and statistical modeling, z-score analysis, and box plots. In this study, a kernel density estimation filter was employed to identify such outliers. The proposed method estimates the probability density of each data point and identifies those that have a probability density below a specified threshold(this paper taken 0.05).  
The filter was applied to the continuous features, including AC1 VV, AC1D.P, AC1 Gsb, AC1 penetration_25 AC1 Dynamic stability, AC2 penetration_25, AC2 VISC_135, AC3 Dynamic stability ESALs (M), and rutting and excluded 38 outliers.  
In theory, the number and structure of input variables can affect the model performance. Studying the structure of the variables and optimizing input variables can help improve the precision of the model and lay a foundation for further research. However, categorical variables cannot be directly read by machine learning models, and character data needs to be converted into numerical data. Instead, they can be processed by one-hot vector encoding. In this study, the presence of a stress-absorbing layer is denoted by 1, whereas its absence is denoted by 0. The missing values refer to data that do not exist in the dataset. Due to limitations in detection conditions, collecting complete data is difficult. For instance, due to sensor factors, temperature data on the day of the test (December 2017) were not obtained. Hence, it was replaced by the temperature data of the day before the test. Values whose eigenvalues deviated significantly from the normal range were deleted. The value ranges and measurement units of the feature values in the original data set differed; therefore, they cannot be directly used for analysis. When the difference in each variable is large, if the original value can be directly used for analysis, the role of the variable with a higher value in the comprehensive analysis would be amplified. Similarly, the variables with lower numerical values would have less effect on the output. Thus, to eliminate the degree of impact, all features were standardized before training. Standardization involves scaling the data to a small interval, removing the unit restriction, and converting it into a dimensionless value. In this study, min-max normalization was adopted for the normalization, and mapping to [0, 1] was then conducted as follows.  
\[z=\frac{(x-x_{min})}{(x_{max}-x_{min})} \tag{9}\]  
where \(z\) is the standardized value, \(x\) is the original data, \(x_{min}\) is the minimum value in the original data, and \(x_{max}\) is the maximum value in the original data.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variables** & **Min** & **Max** & **Mean** & **Std** & **Skew** & **Kurt** \\ \hline AC2 Mr (MPa) & 10,528 & 17,486 & 13,940 & 3310 & 0.0028 & \(-\)1.9102 \\ AC2 passing 4.75 mm (\%) & 24.8 & 32.1 & 25.6368 & 2.0807 & 0.2630 & \(-\)0.7595 \\ AC2 passing 0.075 mm (\%) & 5.4 & 8.4 & 6.3421 & 0.6485 & 1.4389 & 2.8774 \\ AC2 penetration\_25 & 22.2 & 63.4 & 44.8421 & 19.6062 & \(-\)0.2422 & \(-\)1.8696 \\ AC2 VISC\_135 & 0.71 & 2.718 & 1.9356 & 0.7661 & \(-\)0.1036 & \(-\)1.6625 \\ AC3 thickness & 0 & 12 & 7.2631 & 5.1600 & \(-\)0.5472 & \(-\)1.4564 \\ AC3 Mr & 0 & 17218 & 7990 & 5861 & \(-\)0.2806 & \(-\)1.169 \\ Ac3 dynamic stability & 0 & 7701 & 3071 & 2615 & 0.2251 & \(-\)1.2858 \\ Base2 thickness (mm) & 12 & 24 & 18 & 3.8942 & \(-\)0.514 & \(-\)0.8882 \\ Base2 Mr & 2000 & 20,000 & 4986 & 5288 & 2.008 & 2.331 \\ Subbase thickness (mm) & 20 & 48 & 23 & 8.8490 & 1.9649 & 2.0135 \\ SubbaseMr & 300 & 20,000 & 1889 & 4277 & 3.9854 & 13.9700 \\ ESALs(M) & 1.04 & 75.61 & 28.29 & 23.90 & 0.5099 & \(-\)1.1466 \\ Rutting (0.1 mm) & 0 & 132.1 & 65.37 & 23.07 & 0.3191 & \(-\)0.3226 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(Cont.\)