## 5 Time Parameter Selection  
In order to optimize the selection of the temporal parameters to be included in the analysis, we have performed a correlation analysis that allows us to identify and exclude redundant parameters. The correlation matrix presented in Figure 4 illustrates the relationships between various temporal parameters considered in our study. The correlations range from \(-1\) to \(1\), where \(1\) indicates a perfect positive correlation, \(-1\) a perfect negative correlation, and \(0\) no correlation. The network graph in Figure 5 provides a visual representation of the correlations among the temporal parameters, highlighting the strength and direction of the relationships. Figure 4: Correlation matrix of the temporal parameters. Figure 3: Distribution of time parameters in the Gamma-ray (black curve) and proton (orange curve) samples in different SIZE ranges. The matrix highlights several strong correlations among the parameters. For example, \(T\_LAC\_W\) and \(T\_LAC\) show a near perfect correlation (0.98), suggesting that these parameters provide similar information about the temporal structure of Cherenkov showers. Similarly, \(LEN\_ST\) and \(LEN\_ST\_NORM\) also show a very high correlation (0.99), indicating redundancy between these measures. Our feature selection approach focused on systematic redundancy elimination while preserving discriminatory power. When faced with highly correlated parameter pairs (correlation coefficient > 0.90), we retained only one parameter from each strongly correlated cluster. Our selection prioritized parameters with higher feature importance scores in preliminary Random Forest models and those with lower computational complexity. For example, between \(T\_LAC\_W\) and \(T\_LAC\), we selected \(T\_LAC\) due to its marginally higher importance ranking and simpler computational requirements. The final set of eight time parameters was determined through an iterative process that balanced four key criteria:  
* **Diversity in Information**: The chosen parameters cover a broad range of temporal characteristics, from dispersion distributions to time gradients and coherence, ensuring comprehensive representation of shower temporal dynamics. * **Low Redundancy**: Parameters with high correlations to others were excluded to retain only unique and independent features that contribute distinctly to the model's predictive power. * **Feature Importance**: Selected parameters exhibit significant importance scores that justify their inclusion. As shown in the Random Forest feature importance plot (Figure 6), \(LEN\_DT\) and \(LEN\_ST\) are among the top features, indicating their strong predictive power in gamma/hadron separation. * **Practical Considerations**: We preferred parameters that are easier to compute and interpret, such as \(T\_RMS\) and \(LEN\_DT\), over more complex three-dimensional parameters. This pragmatic approach ensures that the model remains efficient for real-time data analysis. While we considered dimensionality reduction techniques such as Principal Component Analysis (PCA), we ultimately opted for direct parameter selection to maintain physical interpretability of the features. This approach preserves the direct connection between each parameter and its underlying physical meaning, which is particularly valuable for understanding the temporal evolution of gamma-ray versus hadron-induced showers. Figure 5: Network graph of the temporal parameter correlations. The application of these criteria resulted in the selection of eight parameters optimized for Gamma/Hadron separation. * _T_RMS_ (Root Mean Square of pixel trigger times): This parameter provides information on the dispersion of the arrival times of Cherenkov photons, which is useful in distinguishing between the more regular photon-induced showers and the more irregular hadron-induced showers. * _T_GRAD_ (gradient of arrival times): This measures the time gradient across the camera, helping to identify the shower orientation and differentiate between gamma and hadron events.