ATD: Topological Data Analysis for Threat Detection

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Change point detection is broadly defined as the problem of identifying instances within a sequence of observations, where changes in the underlying data structure occur. Such changes may be a result of various intentional attacks and other adversaries or may be associated with random failures of the system. The change point detection problem naturally arises in the context of many applications such as crime detection, target tracking, speech recognition, human activity analysis, cybersecurity, financial and environmental monitoring. In turn, understanding hidden data shape and associated shape dynamics is an important step towards more accurate, robust and reliable threat detection and risk analysis under uncertainty and adversarial evasion. One graduate student will be supported each year of this grant.This project proposes novel approaches in this important direction by introducing concepts of topological data analysis and, in particular, persistent homology to characterize, track and test for changes in the data generating process. The proposed formulation at the interface of persistent homology, functional data analysis, and machine learning, offers a broad platform for new data-driven statistical and machine learning methods for automatic detection of attacks, threats, and other anomalies. The ultimate goal of the project is to develop novel geometrically and topologically enhanced procedures for detecting threats in large spatiotemporal data from a variety of sources, and to study their theoretical properties, finite-sample performance, and utility in a broad range of real-world scenarios. The project will offer a number of unique opportunities to facilitate interdisciplinary research training in mathematical sciences, with a particular focus on involving and broadening participation of traditionally underrepresented groups at all educational levels.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.