Group actions and symplectic techniques in Machine Learning and Computational Geometry

机器学习和计算几何中的群行为和辛技术

• 批准号: RGPIN-2017-06901
• 负责人: Fraser, Maia
• 金额: $ 1.82万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634859
• 关键词: Group; actions; symplectic; techniques; Machine

Mathematical tools have become relevant across a broad range of scientific disciplines to an extent never before seen, as our interactions with the world become increasingly data-based and inter-connected. The rising role of topology, geometry and statistics in Computer Science, especially in Data Science, is particularly noticeable. Data are numbers or number-based and so often come with underlying topological, geometric or statistical structure. Understanding how this structure impacts algorithms and properties of interest confers an immediate benefit to algorithmic development, but this innovation requires solid foundations in both Computer Science and Mathematics. My research takes steps to bridge this gap, by applying mathematical tools related to

在从未见过的一定程度上，数学工具已经在广泛的科学学科中变得相关，因为我们与世界的互动变得越来越基于数据和相互联系。拓扑，几何学和统计学在计算机科学（尤其是数据科学）中的作用上升，特别明显。数据是基于数字或数字的，因此经常带有潜在的拓扑，几何或统计结构。了解这种结构如何影响算法和感兴趣的属性为算法开发带来了直接的好处，但是这种创新需要在计算机科学和数学中稳固的基础。我的研究采取了通过应用与