# Outlier Detection and Prediction in Evolving Communities
## 6 Predicting Outlying Behavior of Nodes
### Exploration of Outlier Scores and Future Behavior  
First, we wanted to explore whether there exists a correlation between the current outlier score \(OS\) of a node and its future behavior; that is, we wanted to determine whether nodes with high outlier scores are more likely to leave all communities or even disappear from the network in the next time slices, while nodes with low outlier scores are more likely to join communities and remain in the network in the future, indicating that the proposed outlier score has predictive power. Tables 6 and 7 depict the results of our exploration for the StackExchange and MovieLens datasets, respectively. For each dataset, the nodes were split between those with high (\(OS>0.50\)) and low (\(OS\leq 0.50\)) outlier scores at time point \(t_{i}\), and we examined their community membership at two consecutive time points \(t_{i}\) and \(t_{i+1}\). For each node category, we measured the percentage of nodes that were a member of at least one community and the nodes outside of all communities at each of the two time points. The desirable conclusion after this experiment would be a robust connection between one node's outlier score at the current time point and its community membership at the next time point. In the two tables, we indicate the percentages in bold, with high percentages showing a positive correlation between the outlier score and the nodes' outlying behavior. In Table 6, for StackExchange, it can be observed that, at \(t_{i}\), 41.48% of the nodes with low outlier scores are members of at least one community at the same time point, while at the next time point \(t_{i+1}\)) this percentage increases to 62.04%. This indicates that 62.04% of the nodes with low outlier scores at \(t_{i}\) were community members at \(t_{i}\), a relative increase of 49.55% concerning the percentage of community members at \(t_{i}\). Regarding high outlier score values, we verified a correlation between high outlier score and the probability of a node not being a community member at the next time slice, with a percentage of 72.06% of such nodes. The reduction in the percentage with respect to \(t_{i}\) is due to the nodes that have left the network in \(t_{i+1}\), which are not included in the measurements. Similar conclusions can be drawn for MovieLens, as depicted in Table 7, confirming the predictive characteristics of the proposed outlier score. we follow the traditional outlier definition, labeling a node as an outlier when it does not belong to any communities and as not an outlier when it belongs to at least one community. Three different classifiers were examined: _Support Vector Classification_ (_SVC_), _k-Nearest Neighbors_ with the number of closest neighbors set to 5 (\(kNN5\)), and _Decision Tree Classifier_ (_DT_). We compared the proposed outlier score against widely used structural node features: degree; betweenness centrality, which measures the number of shortest paths going through a node; and PageRank for solving graph-based ranking, as well as combinations of the three. We split the datasets into training and test sets with an 80-20 split, and provided the classifiers with the corresponding input features. In Table 8, we report the F-Score for each of the classifiers and the two datasets when using a combination of different features. In this first experiment, we differentiated between structural features and content to better assess the impact of including content in our problem. Thus, we considered the outlier score as two features, consisting of a structural score and content score. In particular, for each dataset, i.e., the first three result rows, the first part of Table 8 reports results relying solely on the structural feature indicated in the corresponding column, while the second part, i.e., the next three results rows, reports results for each of the corresponding features combined with the proposed content score. Thus, we compare our outlier score against popular structural features as well as against these features enhanced with content-based information.