AF: Small: Collaborative Research: Geometric and Topological Algorithms for Analyzing Road Network Data

该项目旨在开发基于理论的有效方法来分析与道路网络相关的数据——使用表示道路网络的图形作为分析网络数据的框架。由于gps设备的普及，轨迹数据变得无处不在。许多其他来源，包括人口普查数据和犯罪统计，都有地址或地理位置，这些地址或地理位置与基础道路网络相连。将开发具有数学保证的算法，在真实轨迹的自然和现实属性下将轨迹与网络对齐，从轨迹和密度数据重建道路网络。它还将提供两种框架来比较不同级别的数据赋能网络。虽然轨迹对齐、地图重建和地图比较等问题在GIS领域引起了广泛关注，但大多数方法都是临时的，无法提供质量保证，并且仅限于事后分析。本项目将提供新颖的理论基础，结合计算拓扑和几何的方法，并将进一步推进拓扑/几何数据分析领域的最新技术。pi将继续通过该项目将教育和研究活动结合起来。学生将紧密地融入到这个项目的研究和实际实施中，并将在整合几何思维、算法开发和（轨迹）数据分析方面进行训练。这些技能的结合在数据科学中越来越重要。本项目所涉及的主题将丰富这三所院校的课程材料和课程发展。

The project aims to develop theoretically grounded, effective methods for analyzing data associated with road networks -- using graphs that represent road networks as a framework for analyzing network data. Thanks to the spread of GPS-enabled devices, trajectory data has become ubiquitous. Many other sources, including census data and crime statistics, have addresses or geographic locations that link to an underlying road network. Algorithms with mathematical guarantees will be developed to align trajectories to the network under natural and realistic properties of true trajectories, to reconstruct road networks from trajectory and density data. It will also provide two frameworks for comparing data-endowed networks at different levels. While the problems of trajectory alignment, map reconstruction, and map comparison have attracted a lot of attention in the GIS community, most approaches are ad-hoc, provide no quality guarantees, and are limited to post-hoc analysis. This project will provide novel theoretical foundations combining approaches from computational topology and geometry, and will further advance the state-of-the-art of the field of topological / geometric data analysis. The PIs will continue to combine educational and research activities through this project. Students will be tightly integrated into the research and practical implementation of this project, and will be trained in integrating geometric thinking, algorithms development, and (trajectory) data analysis. The combination of such skills is increasingly important in data science. Topics involved in this project will enrich the course material and curriculum development at each of the three institutions.