Geometry and Statistics on Spaces of Dynamical Systems for Pattern Recognition in High-Dimensional Time Series

用于高维时间序列模式识别的动力系统空间的几何和统计

• 批准号: 1335035
• 负责人: Rene Vidal
• 金额: $ 39.1万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1335035&HistoricalAwards=false
• 关键词: Geometry; Statistics; Spaces; Dynamical; Systems

The objective of this project is to develop a mathematical framework for efficiently comparing dynamical systems identified from high-dimensional time-series data as well as algorithms for clustering, classification, and statistical analysis of such data. Dynamical systems are widely used for the analysis, verification, and control of physical, mechanical, thermal, chemical and biological processes. However, there are many emerging applications in which one also needs to "compare the dynamics of two processes". In computer vision, for example, one can use dynamical models to describe kinematic and video data of human motion. While different people move differently, the dynamical models of two people performing the same task (e.g., walking) should be "closer" to each other than the models of two people performing different tasks (e.g., walking vs running). Framework will be developed for spaces of linear dynamical systems whose quotient structure is defined by the action of a group on a smooth manifold. A family of efficiently computable distances in the ambient space will be used to define a family of "group-action-induced distances" in the quotient space. Such distances will be used to develop methods for performing classification, clustering and statistical analysis on spaces of dynamical systems. These methods will be evaluated on kinematic and video data of human activities.The development of methods for comparing dynamical models can impact both basic science and the society at large. In control theory, such methods can impact system identification and robust control. In computer vision, such techniques can be used to discriminate human and crowd activities in video data, which is relevant to many applications in surveillance, security, traffic monitoring, sports coverage/broadcast, human-computer interaction, etc. This project will train engineers and scientist in multidisciplinary research that will need concepts from differential geometry, machine learning, and computer vision. As such, it can potentially impact many other related fields. This project will also impact many diversity outreach activities, including ongoing REU programs, the Women in Science and Engineering (WISE) program and summer camps for K-12 outreach. Datasets and code will be made publicly accessible for research and educational purposes.

该项目的目的是开发一个数学框架，以有效地比较从高维时序列数据以及用于聚类，分类和此类数据统计分析的算法中确定的动态系统。动态系统被广泛用于分析，验证和控制物理，机械，热，化学和生物学过程。但是，有许多新兴应用程序还需要“比较两个过程的动态”。例如，在计算机视觉中，可以使用动力学模型来描述人类运动的运动学和视频数据。尽管不同的人的动态不同，但两个人执行相同任务（例如，步行）的动态模型应与两个执行不同任务的模型（例如，步行与跑步）的模型“彼此接近”。将针对线性动力系统的空间开发框架，其商结构是由组在平滑歧管上的作用定义的。环境空间中有效计算距离的家族将用于定义商空间中的“集体行动诱导距离”家族。此类距离将用于开发针对动态系统空间进行分类，聚类和统计分析的方法。这些方法将对人类活动的运动学和视频数据进行评估。比较动态模型的方法的开发会影响基础科学和整个社会。在控制理论中，这种方法会影响系统识别和强大的控制。在计算机视觉中，这些技术可用于区分视频数据中的人类和人群活动，这与许多在监视，安全性，交通监控，体育范围/广播，人类计算机相互作用等方面的应用相关。该项目将培训多学科研究人员和科学家的多学科研究，这些研究将需要从差异的页面学习，机器学习和计算机视觉中获得概念。因此，它可能会影响许多其他相关领域。该项目还将影响许多多样性外展活动，包括正在进行的REU计划，科学与工程学（WISE）计划（WISE）计划和K-12外展夏令营。数据集和代码将用于研究和教育目的。