Detection of anomalous meetings in a social network

When monitoring interactions within a social network, meetings or contacts between different members of the network are recorded. This paper addresses the problem of using the recorded meetings to determine (a) whether each meeting is anomalous and (b) the degree to which each meeting is anomalous. Performing robust statistical analysis on such data is particularly challenging when the number of observed meetings is much smaller than the number of people in the network. Our novel approach to anomaly detection in this high-dimensional setting is based on hypergraphs, an important extension of graphs which allows edges to connect more than two vertices simultaneously. In particular, the distribution of meetings is modeled as a two-component mixture of a nominal distribution and a distribution of anomalous events. A variational Expectation-Maximization algorithm is then used to assess the likelihood of each observation being anomalous. The computational complexity of the proposed method scales linearly with both the number of observed events and the number of people in the network, making it well-suited to very large networks, and it requires no tuning. The algorithm is validated on synthetic data and it is shown that, for a useful class of distributions, it can outperform related state-of-the-art methods in terms of both detection performance and computational complexity.