# Outlier Detection and Prediction in Evolving Communities
## 2 Related Work
### Outlier Detection
#### 2.2.2 Dynamic Methods  
The survey in [30] provides an overall view of the field, categorizing outlier detection methods for time series, stream data, spatio-temporal data, and temporal networks. The authors observed a lack of methods for online outlier detection, as most window-based methods are offline methods.  
Starting with structural methods, in [31] the authors categorized outliers into global and local outliers, which are respectively differentiated from the network or from their neighbors. Focusing on local outliers, they proposed a corresponding streaming method. In [32], the authors considered a snapshot-based approach for modeling network evolution and proposed the notion of community trend outliers, which evolve in a highly different way compared to other community members. Their model extracts soft patterns from the community evolution procedure and then marks as outliers those nodes that deviate from their best-matching soft pattern in more than one snapshot. Similarly, [33] proposed evolutionary community outliers, or ECOutliers, focusing more on their temporal dimension and how these nodes evolve differently with time. The challenging problem of community matching in a two-snapshot setting was tackled by an objective function that weights the lower contributions made by outliers.  
Continuing with content-based methods, in [34] the authors used an attributed graph with a set of attributes associated with the nodes to determine communities in which members achieve highly topical activity. In this way, they introduced the notion of temporal activeness, inspired by the fact that many nodes may be inactive during several steps of the temporal evolution, as a way to decrease the number of low-activity users in a community by considering a slightly different definition for outliers. In [35], the authors proposed a framework applied to Twitter data to detect sudden rises of emergency topics such as the COVID-19 pandemic. Their method uses k-means to generate a cluster of unusual tweets; however, preprocessing and topic modeling are needed in advance, and the method is not yet suitable for online networks.  
Finally, regarding outlier detection performed on graphs that consider both structure and content, we found a serious lack of related works. This is confirmed by the authors of [36], an exhaustive review of papers corresponding to outlier detection in attributed networks. The authors of this review, much as we do here, distinguished anomaly detection techniques into static and dynamic; each one of these categories was further separated into attributed and unattributed categories. However, although they examined many of state-of-the-art papers, they quoted only static methods. Regarding bipartite graphs, in [37] the authors found groups of possible outliers after tracking the history of employment and disclosures in a real dataset taking the form of a bipartite graph of individual entities and sequentially ordered attributes. The authors searched for groups of outliers, or 'tribes' as they refer to them, which are groups of individuals who share unusual sequences of affiliations. They defined a significance score for each edge, to measure the significance or the anomalousness of shared jobs. Similarly, rather than simply classifying the nodes into outliers, we provide a score that quantifies the outlierness of each node. However, we evaluate each node based on its outlierness, not on the basis of each interaction.  
Table 2 summarizes the works discussed above and compares them concerning: (i) the dimensions they consider, i.e., content and structure; (ii) whether they assign an  
outlier label or score to nodes; (iii) the information (local or global) that they exploit to detect outliers; and (iv) for dynamic methods, whether they are snapshot-based or online.