ATD: Predictive Anomaly Detection for Spatio-Temporal Data with Multidimensional Persistence

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The focus of this project is pattern mining of valuable information from spatio-temporal (ST) data, which is increasingly available through various geo-positioning techniques and critically important for many real-life applications including human mobility understanding, smart transportation, urban planning, public safety, health care, and environmental management. The presence of dependencies among measurements induced by the spatial and temporal dimensions is the main challenge when dealing with ST data. Most modern methods deal with such problems by splitting spatial and temporal dimensions and adding a merge post-processing step which, in turn, leads to the loss of crucial intertwined knowledge among variables. This project will use state-of-the-art theories from machine learning and mathematical topology to simultaneously include spatial and temporal variables within the mining processes, with application to modeling of large ST datasets. Students will be involved in this cross-disciplinary research, which lies at the interface of mathematics, computer science, and data science. The investigators will develop a novel approach to model spatial and temporal interdependencies within ST data by using the most recent techniques of topological data analysis (TDA). The central goal is establishing a new TDA theory, Multi-Persistence, which will better capture shape evolving patterns in ST data with respect to time, and produce a highly expressive unique topological fingerprint of data without splitting spatial and temporal dimensions. The reduced computational cost of calculating topological summaries will permit development of the two-differentiable objects often needed by machine learning (ML) methods and will increase current capabilities to handle large ST datasets. Additional research activities include investigation of the utility of TDA and the new methodology within the context of threat detection tasks for large ST datasets in several settings, such as threat detection in traffic networks, severity predictions, and wildfire research.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.