## 3 Materials and Methods
### Feature Importance with XBoost  
The XGBoost, an improved version of the Gradient Boosting Decision Tree (GBDT) algorithm, has attracted attention due to its ability to operate in parallel and its efficient use of the boosted tree structure. The XGBoost algorithm is designed to enhance the objective function for regression problems by constructing boosted trees [52]. In the XGBoost model shown in Equation (1), F signifies the set of decision trees, while \(n\) represents the number of data points in the dataset. \[y\bar{i}=\sum\limits_{k}^{K}{{fk\ (xi i)}},\ fk\ \in\ F\ (i=1,\ 2,\ \ldots n) \tag{1}\]  
Equation (2) presents the objective function. In this function, \(L\), explained in Equation (3), is a differentiable convex loss function that measures the difference between the estimated value \(y^{n}i\) and the actual value \(yi\). The term \(\Omega\) denotes the regularization term, which serves to avoid overfitting by applying smoothing regularization [53]. \[Obj=L+\Omega \tag{2}\]  
\[L=\sum\limits_{i=1}^{n}{(y\bar{i}-yi)^{2}} \tag{3}\]  
The XGBoost assesses the importance of a feature using three metrics. The gain metric quantifies how much a feature reduces the error in the model's splitting decisions within a tree. The frequency metric mirrors how often a feature is used in the model's split decisions. The cover metric represents the average number of observations influenced by a feature at each split point in the decision tree. In this study, feature importance was assessed using the gain metric of the XGBoost algorithm. The XGBoost is a model based on gradient-boosted decision trees. The significance of a feature can also be interpreted in terms of how much the model's predictive performance changes when that feature is randomly perturbed [54]. To understand the value of situational and meteorological features in passenger count prediction, the XGBoost model was employed. The model's hyperparameters were adjusted to minimize the RMSE error metric, as presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline
**Input Variables** & **Encoded Values** & **Descriptions** \\ \hline xM (Month) & 1–12 & January–December \\ xS (School days) & 0–1 & 0: non-school day; 1: school day \\ xNH (National Holiday) & 0–1 & 0: not a national holiday; 1: national holiday \\ xD (Days of the month) & 1–31 & 31 days per month \\ xWeek (Days of the week) & 1–7 & Monday–Sunday \\ xH (Hour) & 0–23 & 24 h per day \\ xTemperature & Actual & Hourly temperature (\({}^{\circ}\)C) \\ xSnow & Actual & Hourly snowfall (cm) \\ xRain & Actual & Hourly rainfall (mm) \\ xHumidity & Actual & Hourly humidity (\%) \\ xWind & Actual & Hourly wind speed (m/sn) \\ xCloudiness & Actual & Hourly cloud cover (okta) \\ \hline Output Variables & Encoded Values & Descriptions \\ \hline xBus & Actual & Hourly bus passenger flow \\ xRail & Actual & Hourly rail passenger flow \\ \hline \end{tabular}
\end{table} 
Table 2: Description of input variables used in the models. As shown in Figure 6, the hour variable appeared as the most important feature. This was followed by school days, day of the week, public holidays, and month. Among meteorological variables, humidity, temperature, and wind speed had relatively lower importance compared to time-related variables. Precipitation, snow depth, day of the month, and cloud cover were identified as features with the lowest importance. In deep learning-based approaches, improving predictive accuracy and reducing model complexity by eliminating unnecessary parameters is essential. Therefore, based on the feature importance ranking, the variables that contributed most significantly--hour, school days, day of the week, public holidays, month, humidity, temperature, and wind speed--were selected as input features for the modeling process. The limited influence of precipitation- and snow-related variables may be attributed to the relatively low number of rainy or snowy days during the study period.