AF: Small: Expanding the Reach of Topological Data Analysis

AF：小：扩大拓扑数据分析的范围

• 批准号: 2007961
• 负责人: Tamal Dey
• 金额: $ 35万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2020-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2007961&HistoricalAwards=false
• 关键词: AF; Small; Expanding; Reach; Topological

Data science and analysis have taken a center stage in modern years for a swath of applicationsembracing daily life. In general, AI and machine learning have been the backbone of thisdevelopment. Recently, a technique based on the classical mathematical area of topology has evolvedthat is showing promise to complement and in some cases be an alternative to AI techniques. As thisemergent area, known as topological data analysis (TDA), expands its reach, the task of extractingintelligent summaries out of diverse, complex data becomes increasingly challenging. To meet thischallenge, TDA also needs to expand its current repertoire of techniques by making further anddeeper connections between mathematical and algorithmic concepts. This project aims to developthese techniques while training graduate students and other workforce in data science as aconsequence.The project, in particular, will investigate several novel mathematical concepts in conjunction withcomputations to address various challenges appearing in the following topics: (i) augmentingtopological summarization with geometry, (ii) connecting discrete Morse theory to furtherapplications, (iii) developing persistence theory for combinatorial dynamical systems, and (iv)developing multi-parameter persistence from a computational view-point. A successful algorithmictheory supported by sound mathematics for the four aforementioned themes can provide a powerfultool for data exploration and analysis in a spectrum of engineering and scientific fields. Theproposed outreach activities will also further consolidate the ongoing effort of bringing togetherdifferent communities in science and engineering engaged into modern data analysis. The projectwill help train graduate students who will develop skills in mathematics and theoreticalcomputer science, most notably in algorithms and topology, in writing efficient and usable software,and in its application to analyzing real-world data sets. Efforts will be made to recruit and mentorstudents from under-represented groups, as has already been done by the investigator.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.

数据科学和分析已在现代占据了中心地位，以促进日常生活的大量应用。通常，AI和机器学习一直是这一开发的骨干。最近，基于拓扑的经典数学领域的一种技术已经发展出了补充的希望，在某些情况下是AI技术的替代方法。随着此Emergergent区域（称为拓扑数据分析（TDA））扩大了其影响力，从各种各样的摘要中提取摘要的任务越来越具有挑战性。为了满足智利，TDA还需要通过在数学和算法概念之间建立进一步的和深层的联系来扩展其当前的技术曲目。 This project aims to developthese techniques while training graduate students and other workforce in data science as aconsequence.The project, in particular, will investigate several novel mathematical concepts in conjunction withcomputations to address various challenges appearing in the following topics: (i) augmentingtopological summarization with geometry, (ii) connecting discrete Morse theory to furtherapplications, (iii) developing persistence theory for combinatorial dynamical systems, （iv）从计算观点开发多参数持久性。在上述四个主题上支持声音数学支持的成功算法理论可以为在工程和科学领域的范围内提供强大的数据探索和分析。所采用的外展活动还将进一步巩固持续的努力，即将参与现代数据分析的科学和工程领域不同的社区聚集在一起。该项目将帮助培训将发展数学和理论记录科学技能的研究生，最著名的是算法和拓扑，撰写有效且可用的软件，以及其用于分析现实世界数据集的应用。正如调查员已经完成的那样，将努力从代表性不足的群体中招募和指导学生。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子和更广泛的影响评估标准，认为值得通过评估来获得支持。