# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 5 Results
### Fixed Decision Threshold  
The previous results showcase the model's performance as a function of the decision threshold, i.e., the threshold used to binarize the model prediction. To assess the performance of individual samples in terms of the tangible metrics of \(F1\), \(P\), and \(R\), a decision threshold must be established. As mentioned before, this threshold plays a crucial role in the final performance, as it involves a trade-off between detecting all encounters with some false positives and detecting only a subset of true encounters. Previous insights also underscore the strong relationship between the decision threshold and the distance threshold. The following results present the model's performance when the decision threshold aligns with the normalized distance threshold used to binarize the ground truth, namely \(T=1500\) km with a decision threshold of 0.75, \(T=2000\) km with a decision threshold of 0.5, and \(T=2500\) km with a decision threshold of 0.25. Figure 9 presents a comparative analysis between true and predicted post-processed encounters across three satellite pairs in both synthetic and realistic datasets. Each dataset features three distinct scenarios corresponding to three different \(T\) values (to binarize the ground truth) and three different decision thresholds (to binarize the model prediction). As expected, both true and predicted contact durations increase as the thresholds, expressed in kilometers, increase. The results indicate that the model is able to generalize the encounters for these six unseen samples, even in complex scenarios characterized by intermittent encounters, such as those observed in synthetic pair 4-6 and Celestrak pair 0-5. However, some missed and false communication opportunities can be observed, particularly in synthetic satellite pair  
Figure 9: True post-processed encounters (in blue) and post-processed model prediction (in orange) across three different distance thresholds. (**a**) Synthetic data, \(T=1500\) km, decision threshold of 0.75. (**b**) Synthetic data, \(T=2000\) km, decision threshold of 0.5. (**c**) Synthetic data, \(T=2500\) km, decision threshold of 0.25. (**d**) Celestrak data, \(T=1500\) km, decision threshold of 0.75. (**e**) Celestrak data, \(T=2000\) km, decision threshold of 0.5. (**f**) Celestrak data, \(T=2500\) km, decision threshold of 0.25. 0-9, where the contact around hour 42 shown in Figure 9a is lost, and the contact around hour 40 shown in Figure 9a persists longer than expected. Moreover, in Figure 9d, Celestrak pair 0-1 exhibits a predicted encounter that initiates and concludes several minutes earlier than the true encounter. To quantify these results, Figure 10 shows, for each scenario, the distribution of \(F1\) and the Balance Accuracy (\(BA\)) across all samples in both test datasets. The \(BA\), as defined in Equation (7), is the average of sensitivity and specificity. The sensitivity (or the True-Positive Rate (\(TPR\))) is the same as the \(R\), while the specificity (or True-Negative Rate (\(TNR\))) assesses the model's effectiveness in correctly excluding the negative instances. Notice that specificity is another way of measuring the wasted energy of the prediction, since it accounts for the number of \(FP\)s.  
\[BA=\frac{TPR+TNR}{2}=\frac{1}{2}\bigg{(}R+\frac{TN}{TN+FP}\bigg{)} \tag{7}\]  
Note that certain pairs exhibit an \(F1\) score of zero. Upon closer examination of these critical pairs, it is observed that they are characterized by sporadic encounters (e.g., a single and short communication opportunity throughout the entire duration). In such critical scenarios, obtaining zero \(TP\)s is almost inevitable, and a single \(FP\) or \(FN\) results in an overall \(F1\) score of zero, thus significantly impacting the average performance across all samples. However, in these critical situations where \(TP\) equals zero, \(BA\) achieves a maximum value of 0.5 when \(FP\) is also zero.