# Predicting Putting Development Using Machine Learning Methods Based on RIOCHTrack Data
## 3 Results and Discussion
### Analysis of Feature Importance Based on SHapley Additive exPlanations (SHAP)  
The analysis of rutting influencing factors can help prevent rutting by controlling key factors. The analysis of feature importance can serve as a simple and effective method for elucidating the interaction between feature and target variables. In order to improve the interpretability of the model, it is necessary to further quantify the impact of feature parameters on rutting performance, and provide more specific guidance for road maintenance management measures. SHAP can provide global and local explanations for the prediction results of GBDT models. Compared with the traditional feature importance based on RF, SHAP can not only rank the importance of each feature affecting the model but also reflect how the features affect the results and their impact trends.  
The SHapley Additive exPlanations (SHAP) framework presents an alternative method for evaluating the contributions of various features. It combines game theory principles with local explanations to provide a comprehensive analysis. SHAP can accurately determine the contribution of each feature (\(\Phi_{\text{i}}\)) to the predicted value (\(f_{\text{x}}\)) by utilizing the concept of marginal contribution. The formula for calculation is as follows:  
\[\Phi_{\text{i}}=\sum_{S\in N\{i\}}\frac{|S|!(n-|S|-1)!}{n!}[f_{x}(S\cup\{i\})- f_{x}(S)] \tag{16}\]  
The output target is defined as a linear addition of input features, which can be expressed as:  
\[g(x)=\phi_{0}+\sum_{i=1}^{m}\phi_{i}x_{i} \tag{17}\]  
Figure 12 shows scatter density plots of SHAP values of each influence factor. In this graph, each point represents the Shapley value of a feature and a single observation in the dataset [37]. The position of each dot on the \(x\)-axis represents the Shapley value assigned to each factor, which indicates its influence on the pavement rutting. Positive values indicate a positive impact, while negative values indicate a negative impact. Additionally, the \(y\)-axis provides the factors in their order of importance. The color in Figure 12 represents the values of the factors. For instance, with the high value of base modulus, the asphalt rutting is lower, which indicates us increasing the stiffness of the base is beneficial for reducing rutting depth. However, the influence of ESALS is inverse. The larger the value of ESALS, the value of rutting increases. Feature importance analysis revealed that the material of the asphalt pavement surface layer has a greater contribution to rutting than that of the base and subbase layers. Therefore, rutting research in the future should focus on the performance of surface materials.  
In addition to global interpretation based on the entire dataset, the SHAP method also provides local interpretation for individual samples. Figure 13 shows the Shaply corresponding to each feature and the process from the base value to the final output. In Figure 13, the length of the bar indicates the degree of significance, while the color represents the direction (negative or positive) of each factor's effect. The mean of the prediction outs is a baseline. It can be seen that ESAL is the most significant factor in infecting rutting.