A Nonparametric Approach to Uncovering Connected Anomalies by Tree Shaped Priors

The area of anomaly detection has recently been expanded in the graph-based data. Anomalous vertices are often exhibited as a connected subgraph. Few works, however, have focused on connected anomalous subgraph detection because of the challenge of optimizing graph functionals under connectivity constraints. We employ Non-Parametric Graph Scan (NPGS) statistics for detecting anomalies within graph-based data. Based on the NPGS statistics, we proposed an efficient approximate approach to the connected anomalous subgraph detection problem that provides provable guarantees on performance and quality. In particular, we first decompose the problem into a sequence of subproblems, each of which can be reduced to a Budget Price-Collecting Steiner Tree (B-PCST) problem, and then develop efficient exact and approximate algorithms for a special category of graphs in which the anomalous subgraphs can be reformulated in a fixed tree topology. Our method has a wide variety of applications, such as disease outbreak detection, road traffic congestion detection, and event detection in social media, because the NPGS statistics is free of distribution assumptions and can be applied to heterogeneous graph data.