Anomaly Detection Using Persistent Homology

Many aspects of our daily lives now rely on computers, including communications, transportation, government, finance, medicine, and education. However, with increased dependence comes increased vulnerability. Therefore recognizing attacks quickly is critical. In this paper, we introduce a new anomaly detection algorithm based on persistent homology, a tool which computes summary statistics of a manifold. The idea is to represent a cyber network with a dynamic point cloud and compare the statistics over time. The robustness of persistent homology makes for a very strong comparison invariant.