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

现代应用程序中的海量数据在存储、处理和挖掘数据方面带来了挑战。 此外，数据集通常是分布式的，因此没有一个数据中心可以提供所有相关数据进行分析。 新的数学和统计算法需要用于分析分布式数据库，特别是由时空数据组成的数据集。 该项目旨在应对如此庞大的数据集所带来的挑战，以更好地了解人类动态。 该项目有可能以多种方式造福社会。 首先，通过开发更准确和有效的数学算法来处理分布式时空数据，该项目的结果可以导致改进的异常和威胁检测。其次，该项目将通过培训研究生、课程开发和外联活动，促进STEM劳动力的发展。 第三，该项目的结果将为公共实体和其他利益攸关方纳入异常检测的新算法提供途径，特别是在交通网络和食品安全方面。第四，该项目将解决研究的伦理，法律的和社会影响，特别是社会对数据收集和分析的关注。该项目旨在开发一个算法工具包，适用于各种时空数据集，用于解决分布式测量环境下的非欧几里德回归问题。该工具包将以Kaczmarz算法为基础，这是一种求解线性方程组的迭代分布式方法。 该项目将涉及建立新算法的理论基础，以及保证其效率或开发有效的近似算法。 该项目将利用这一用于解决非欧几里德回归问题的新型算法工具包来设计新型异常检测算法，包括基于图的时空数据集异常检测的新方法，这些方法将应用于涉及人类动力学的问题，如交通网络和食品安全。 该项目将通过调查公众对数据处理系统的信任和支持，并通过研究补充社会科学方法解释公众反应和意见的程度，来解决新结果的伦理、法律的和社会影响。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.