Pointwise anomaly detection and change detection focus on the study of individual data instances however group deviation research involves groups or collections of observations. Data instances are inherently clustered into groups and groups that deviate from the expected pattern are important in applications such as high energy particle physics to healthcare collusion. Group deviation detection techniques result in novel research discoveries, mitigation of risks, prevention of malicious collaborative activities and other interesting explanatory insights. In particular, static group anomaly detection is the process of identifying groups that are not consistent with regular group patterns while dynamic group change detection assesses significant differences in the state of a group over a period of time. Since both group anomaly detection and group change detection share fundamental ideas, this thesis provides a clearer and deeper understanding of group deviation detection research in static and dynamic situations.
There are many ways to approach the problem of detecting groups that deviate from the expected pattern. One way to detect group deviations involves characterising regular group behaviours by certain features then applying traditional detection methods. For static group anomaly detection with image applications, we focus on directly applying discriminative machine learning models to detect anomalous groups using deep generative models. Whereas in the application of dynamic group change detection, we formulate an algorithm that sequentially detects statistically significant deviations (abrupt change-points) in a variety of statistical properties of a group monitored over time. We further discuss the advantages and limitations of our proposed methods for detecting group deviations for different scenarios.