ATD: Efficient and Stable Algorithms for Non-Euclidean Regression in Discrete Geometries

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The immense amount of data at hand in modern applications creates challenges in storing, processing, and mining the data. Furthermore, datasets often are distributed, so that no single data center has all relevant data available to analyze. New mathematical and statistical algorithms are needed for analyzing distributed databases, particularly datasets that consist of spatiotemporal data. This project aims to address challenges posed by such massive datasets in an effort to better understand human dynamics. This project has the potential to benefit society in several ways. First, by developing more accurate and efficient mathematical algorithms for processing distributed spatiotemporal data, the project results can lead to improved anomaly and threat detection. Second, the project will contribute to STEM workforce development through training of graduate students, curriculum development, and outreach activities. Third, results of the project will provide avenues for incorporation of new algorithms for anomaly detection to public entities and other stakeholders, particularly in the context of transportation networks and food safety. Fourth, the project will address the ethical, legal, and societal impacts of the research, especially societal concerns regarding the collection and analysis of data.This project aims to develop a toolkit of algorithms, applicable to a wide variety of spatiotemporal datasets, for solving non-Euclidean regression problems in the context of distributed measurements. The toolkit will be based on the Kaczmarz algorithm, an iterative, distributed method for solving systems of linear equations. The project will involve both establishing the theoretical foundations of the novel algorithms as well as guaranteeing their efficiency or developing efficient approximate algorithms. The project will leverage this novel toolkit of algorithms for solving non-Euclidean regression problems to design novel anomaly-detection algorithms, including new methods for anomaly detection in graph-based spatiotemporal datasets, which will be applied to problems involving human dynamics such as transportation networks and food safety. The project will address the ethical, legal, and societal impacts of new results by investigating public trust in and support for data processing systems by examining the extent to which complementary social science approaches explain public responses and opinions.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.