## 2 Materials and Methods
### Training, Testing, and Results of the ML Model  
This study investigates the impact of position accuracy and the temporal intervals between campaigns on GNSS velocity accuracies for each component using machine learning techniques. The dataset is partitioned into two groups, corresponding to the East (E) and North (N) velocity components. For the E component, the independent variables (features) are Se1, Se2, and Se3, representing year intervals, while the dependent variable (target) is Swe. Similarly, for the N component, the independent variables are Sn1, Sn2, and Sn3, with Svn as the dependent variable. Both datasets are complete and contain no missing values (Table 1). The data were partitioned into training (80%) and testing (20%) subsets. Four regression models--SVM, MLR, RF, and KNN--were implemented using the Scikit-Learn library in Python 3.10.0. The Elbow method was utilized to determine the optimal number of neighbors for the KNN algorithm, yielding values of 10 and 7 for the E and N components, respectively (Figure 3). During model training, k-fold (k = 5) cross-validation was employed [40]. Model performance, including training and testing scores, along with key evaluation metrics, is summarized in Table 3. Additional performance metrics that are commonly used in the literature were also evaluated, yielding comparable results [41]. Figure 3: Number of neighbors determined for KNN according to elbow method. The results presented in Table 2 indicate that the RF algorithm delivered the most accurate performance for both the E and N components. The training and testing scores for both components exceeded 95%, with an average RMSE of approximately \(\pm\)0.1 mm/year. Additionally, k-fold cross-validation results for the RF algorithm demonstrated training and testing scores above 90%, suggesting robust generalization and reliable performance on real-world data. In comparison, the SVM and KNN algorithms achieved training scores above 91% for both components, with test scores ranging from 86% to 91%. However, the average RMSE values for these algorithms were higher at approximately \(\pm\)0.3 mm/year. Notably, their k-fold cross-validation scores, which fall below 79%, reveal a discrepancy between the training/testing performance and generalization capability. This indicates that the optimistic results observed during training and testing might not hold consistently for unseen data, highlighting the potential for greater error in real-world applications. The MLR algorithm, which performed the weakest among all methods, achieved training and testing scores between 72% and 76% for both components, with its average RMSE values ranging from \(\pm\)0.4 to \(\pm\)0.5 mm/year. The k-fold cross-validation results for MLR align closely with its training and testing scores, falling within the 70-75% range. This consistency suggests that while MLR exhibited lower predictive accuracy, its performance was stable across datasets. To evaluate the performance of all algorithms on the test data, the residuals (differences between the reference values and the predicted values) were calculated. The reference values (velocity accuracies) and residuals for each algorithm were visualized using dual vertical axes to enhance resolution and clarity (Figures 4-7). The visualizations were created using Python's Matplotlib library. Figure 5: Reference velocity accuracies and the residuals in KNN for test dataset (The red line represents the referenced GNSS velocity accuracies, while the blue line represents the residuals). Figure 6: Reference velocity accuracies and the residuals in SVM for test dataset (The red line represents the referenced GNSS velocity accuracies, while the blue line represents the residuals). Figure 7: Reference velocity accuracies and the residuals in MLR for test dataset (The red line represents the referenced GNSS velocity accuracies, while the blue line represents the residuals).