# Evolutionary Features for Dynamic Link Prediction in Social Networks
## 3 Network Datasets and Experimental Settings
### Performance Evaluation
In addition to accuracy measures, AUCROC (Area Under Receiver Operating Characteristics Curve) and AUCPR (Area Under Precision-Recall Curve) were also used to measure the classification performance. While the AUCROC measure is the de facto standard for measuring supervised learning-based classification, AUCR is reported for a more differentiated view regarding the learning task in the imbalanced dataset. Despite its criticism [54], AUCROC is a popular metric (after accuracy) used in binary classification. Accuracy only classifies the class label as right or wrong; however, AUCROC quantifies the uncertainty associated with classifiers by introducing a probability value. It is essentially equivalent to average precision, which is another common measure for ranking results ([PERSON] et al. 2008) [55], and it relates the true positive rate against the true negative rate of a classifier. As an important traditional measure, it is also used in imbalanced classification problems. AUCROC score interprets the probability that a randomly chosen missing link in the test phase belongs to \(G_{T+1}\) is given higher probability score than a randomly chosen non-existent link, which is absent both in the training \(G_{T}\) and test network \(G_{T+1}\). The calculation of AUCROC is given as defined by the formula AUCROC\(=\frac{(n^{\prime\prime}+0.5n^{\prime\prime})}{\pi}\), where \(n\) denotes the number of independent comparisons, \(n^{\prime}\) denotes the times where a missing link in the test network has been given a higher score, and \(n^{\prime\prime}\) denotes the times when a non-existent link has been given a higher score. AUCROC curve demonstrates how the number of correctly classified positive examples varies with the number of incorrectly classified negative examples and shows an overly optimistic view of an algorithm's performance in the presence of large skew in the class distribution where the precision-recall curve was proposed as an alternative to ROC in such cases. This is because a large change in the number of false positives can make a small change in the false positive rate (i.e., \(\frac{FP}{FP+TN}\)) that is used in constructing the ROC curve. Precision compares false positives to true positives instead of true negatives and captures the effect of many negative examples impacting the algorithm's performance. Furthermore, for a given ROC curve, the corresponding P-R (precision-recall) curve varies with skewness in the class distribution. Therefore, [PERSON] et al. [56] recommended that the area under the precision-recall curve (AUCPR) often serves as a summary statistic while comparing the performances of several different algorithms. The authors also proposed a method to determine the minimum value of AUCPR as \(AUCPR_{min}=1+\frac{(1-\pi)ln(1-\pi)}{\pi}\) with skew \(\pi=\frac{\#positivesamples}{\pi}\), where \(n=\) total number of samples in the classification dataset. According to this equation, considering the ratio of positive and negative samples as 1:10 (i.e., the ratio of positive and negative samples is 1:10 in this study) in the classification datasets of the directed and undirected networks and the value of the skew \(\pi=0.091\), the minimum value of AUCPR in these datasets should be 0.04. However, for the rest of the three networks (i.e., \(G_{ph}\) and \(G_{th}\)), since the skew \(\pi=0.33\) (i.e., ratio 1:2), the minimum value of AUCPR should be 0.189. For sake of comparison, this study compared the performances of dynamic features with a well-known metric, 'Resource Allocation' [57], which is widely used for link prediction purposes in static networks and demonstrated improved performance. We also implemented the link prediction strategy in dynamic networks proposed by [PERSON] and [PERSON] [34], where the authors built a time series of traditional topological metrics (e.g., Commonwealths) for non-connected actor pairs for each SIN in the training phase.