## 4 Results and Discussion
### Clustering Analysis (DBSCAN) and Discussion  
As described in Section 3.2.3, an adapted version of the DBSCAN algorithm optimized with KD-Tree was used for the clustering analysis. This approach was chosen due to computational limitations arising from the size of the complete dataset (approximately 1,400,000 records). To ensure the feasibility of the analysis without sacrificing representativeness, an initial sample of 17,951 records was used, weighted with expansion factors reflecting the statistical distribution of the total population. \"Waiting Time\" and \"Mode of Transport\" were exclusively selected because they describe operational attributes of the service, independent of travelers' socioeconomic characteristics. In preliminary tests, the inclusion of additional variables (such as demographic or socioeconomic data) within the algorithm degraded cluster quality (silhouette coefficient < 0.15), blurring the distinction between trips with long and short waits and, consequently, reducing the interpretability and usefulness of the results. However, socioeconomic variables were applied ex post--outside the algorithm--to characterize each cluster. Selection of eps_value and min_samples Parameters: Calibration of eps_value and min_samples followed an iterative approach. Ranges of eps_value from 0.1 to 1.0 and min_samples from 5 to 50 were tested. Low eps_value values (<0.3) generated excessive noise (>50%) and fragmented clusters, whereas higher values (>0.7) merged heterogeneous groups. Regarding min_samples, values above 30 eliminated small yet significant clusters, and values below 10 increased noise. After evaluating internal cohesion using the silhouette coefficient, eps_value = 0.5 and min_samples = 20 were selected, achieving a balance between robustness and granularity in cluster formation. KD-Tree Implementation With Expansion Factors: In the implementation, expansion factors were incorporated as weights into the KD-Tree density calculation, ensuring each point reflected its representativeness in the total population. This strategy preserved the statistical fidelity of the clusters with respect to the actual transport system. Furthermore, KD-Tree optimization substantially reduced computational complexity, allowing efficient handling of weighted data volumes without compromising analysis quality. Cluster Characterization  
Using the adapted DBSCAN algorithm, clustering analysis identified user groups with similar patterns in waiting time and transport mode in Greater Valparaiso. With a weighted silhouette coefficient of 0.7247, the robustness and internal consistency of the resulting clusters were confirmed, indicating that waiting time patterns and transport modes were meaningfully captured. A total of nine clusters were identified, along with a group of points classified as noise. Table 7 summarizes the main characteristics of each cluster. It is important to note that cluster \(-1\) encompasses points that the DBSCAN algorithm classified as noise. These points do not meet the specified density criteria and, therefore, are not assigned to any particular cluster. Although they represent a small proportion of the dataset, their inclusion in the analysis provides a complete view and accounts for possible outliers or cases that do not follow the general patterns. To clarify the analysis, clusters were grouped into three categories based on waiting times, as detailed in Table 8.  
1. Clusters with Low Waiting Times. These clusters represent users whose waiting times are below the overall average, indicating greater transport service efficiency. Commonly used modes of transport in these clusters include funicular (Cluster 7), trolleybus (Cluster 5), Taxi Colectivo (Cluster 1), and Metro Valparaiso (Cluster 2). The most frequent home macrozones are Valparaiso Alto and Villa Alemana Norte. The users in these clusters are mainly employees or workers and students, suggesting that these efficient modes of transport are used for both work-related and educational purposes. 2.