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

该项目的重点是从时空(ST)数据中挖掘有价值的信息，这些信息通过各种地理定位技术日益可用，对于许多现实生活中的应用至关重要，包括人类移动性理解、智能交通、城市规划、公共安全、医疗保健和环境管理。在处理ST数据时，存在由空间和时间维度引起的测量之间的相关性是主要挑战。大多数现代方法通过分离空间和时间维度并增加合并后处理步骤来处理这类问题，这反过来又导致变量之间关键的相互交织的知识的丢失。该项目将使用机器学习和数学拓扑学的最新理论，在挖掘过程中同时包括空间和时间变量，并应用于大型ST数据集的建模。学生将参与这项跨学科的研究，它位于数学、计算机科学和数据科学的交界处。研究人员将开发一种新的方法，通过使用最新的拓扑数据分析(TDA)技术来模拟ST数据中的空间和时间相互依赖关系。中心目标是建立一种新的TDA理论--多持久性，该理论将更好地捕捉ST数据中形状随时间的演变模式，并在不分割空间和时间维度的情况下生成高度可表达的唯一数据拓扑指纹。计算拓扑摘要的计算成本的降低将允许开发机器学习(ML)方法经常需要的两个可区分对象，并将增加当前处理大型ST数据集的能力。其他研究活动包括在几种环境下对大型ST数据集的威胁检测任务的背景下TDA的效用和新方法的调查，例如交通网络中的威胁检测、严重性预测和野火研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.