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

该项目的重点是从时空（ST）数据中挖掘有价值信息的模式，这些信息越来越多地通过各种地理定位技术获得，对许多现实生活中的应用至关重要，包括人类移动理解、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，空间和时间维度引起的测量之间存在依赖关系是主要挑战。大多数现代方法通过分割空间和时间维度并添加合并后处理步骤来处理此类问题，这反过来又导致丢失变量之间交织在一起的关键知识。该项目将使用来自机器学习和数学拓扑的最先进理论，同时包括采矿过程中的空间和时间变量，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界面。研究人员将通过使用最新的拓扑数据分析（TDA）技术，开发一种新的方法来模拟ST数据中的空间和时间相互依赖性。中心目标是建立一个新的TDA理论，即Multi-Persistence，该理论将更好地捕获ST数据中与时间相关的形状演变模式，并在不分割空间和时间维度的情况下产生高度表达的独特数据拓扑指纹。计算拓扑摘要的计算成本降低，将允许开发机器学习（ML）方法经常需要的双可微对象，并将提高当前处理大型ST数据集的能力。其他研究活动包括调查TDA的效用，以及在几种设置下大型ST数据集的威胁检测任务背景下的新方法，例如交通网络中的威胁检测、严重性预测和野火研究。该奖项反映了美国国家科学基金会的法定使命，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 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.