# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 5 Results
### Fixed Distance Threshold
behavior emerges as a result of increasing the distance threshold (\(T\)): the number of true encounters rises as the encounter duration increases, transforming some \(F\)Ps into \(T\)Ps but some \(T\)Ns into \(FN\)s. In this case, the positive effect on both \(F\)Ps and \(T\)Ps is reflected in a larger area under the \(P\) curve, while the increase in \(FN\)s is strong enough to observe a decrease in the area under the \(R\) curve. However, it can be concluded that the positive effect outweighs the negative one, as evidenced by the increase in the area under the \(F1\) curve with the distance threshold. Moreover, the imbalance within the ground truth, characterized by significantly more lower values compared to higher ones, presents challenges for the model in accurately predicting encounters associated with higher \(T\) values. Comparing the results obtained with the two distinct datasets, it can be observed that the Celestrak dataset demonstrates superior performance across all scenarios. This behavior comes from the distinct characteristics of each dataset. In the synthetic dataset, satellites are uniformly distributed, whereas real satellites from Celestrak tend to be densely clustered within specific regions and constellations. This non-uniform distribution results in longer satellite encounters and, consequently, a better balance between positive (1) and negative (0) instances. A higher level of dataset balance facilitates prediction. Additionally, Figure 7 shows that the decision threshold linked to the highest performance hardly depends on the scenario, as it decreases with increasing \(T\). However, selecting the optimal decision threshold does not only depend on \(T\) but is also a trade-off between detecting all the communication opportunities (but some \(F\)Ps) and detecting only true opportunities (but some \(FN\)s). This decision is left to the final user. Nevertheless, an interesting point is found in the intersection between the \(P\) and \(R\) curves, representing the maximum F1 score. Generally, these curves intersect when the decision threshold aligns with the normalized distance threshold (red dashed line) applied to the ground truth. This indicates the good behavior of the model. A similar and commonly employed metric for assessing the performance of a binary predictive model without specifying a decision threshold is the average precision (AP), measured as the area under the Precision-Recall Curve (PRC). Figure 8 illustrates the PRC for each scenario and dataset. In line with previous observations, it is noted that the AP of the Celestrak dataset surpasses that of the synthetic dataset by approximately 6% to 4%. These results also highlight the upward trend with the distance threshold, corresponding to an increase in the number of true encounters accompanied by a decrease in \(F\)Ps and a simultaneous rise in \(T\)Ps. Figure 8a showcases the most challenging scenario characterized by the highest degree of imbalance in the ground truth with \(T\) = 1500 km. It features minimum AP values for the synthetic and Celestrak datasets of 83% and 89%, respectively. Conversely, the scenario with the highest \(T\), as illustrated in Figure 8c, achieves a maximum synthetic AP of nearly 92%, escalating to 96% with the Celestrak dataset. Figure 8: Precision and recall curves obtained using both synthetic and Celestrak test sets across three different distance thresholds. The average precision, representing the area under the curves, is also indicated. Additionally, points denote the precision and recall values corresponding to the maximum F1 score. (**a**) \(T\) = 1500 km. (**b**) \(T\) = 2000 km. (**c**) \(T\) = 2500 km.