ATD: Geometric and Statistical Data Analysis on Special Manifolds for Threat Detection

ATD：用于威胁检测的特殊流形的几何和统计数据分析

• 批准号: 1120875
• 负责人: Michael Kirby
• 金额: $ 12.7万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1120875&HistoricalAwards=false
• 关键词: ATD; Geometric; Statistical; Data; Analysis

This proposal concerns the development of new geometric algorithms for detecting and classifying threats from airborne biological agents and chemical agents. The investigators propose a mathematical framework centered on encoding massive data sets associated with streaming hyperspectral imagery as points on special manifolds, e.g., as representations on Grassmann, Stiefel as well as flag manifolds. In this setting, algorithms will be developed for computing descriptive statistics. A well-known example of such an algorithm was introduced by Karcher to compute the mean of a set of points on a Grassmann manifold. The investigators are primarily concerned with developing new algorithms with improved computational properties on Grassmannians, as well algorithms that can be applied to, e.g., Stiefel and flag manifolds. These algorithms will be designed to be applied to very large data sets in real time and will be evaluated using temporally-evolving hyperspectral data sets made available by the Defense Threat Reduction Agency. These include (but are not limited to) data acquired using a Fabry-Perot Interferometer and Frequency Agile Lidar.The proposed interdisciplinary research program addresses a major challenge related to National Security, i.e., identifying and assessing chemical and biological risks in the environment from observational data in real time. New mathematical tools for exploring massive quantities of chemical and biological hyperspectral data are proposed to assist with threat detection and characterization. A primary goal of the research program is to apply these tools to exceed performance capabilities of current techniques used for classification of biological and chemical threats. It is anticipated that the results of this research program will be useful to other applications related to National Security such as detection of anomalies in data beyond hyperspectral imagery.

这项提议涉及开发新的几何算法来检测和分类来自空中生物毒剂和化学毒剂的威胁。研究人员提出了一个数学框架，其中心是将与流式高光谱图像相关的海量数据集编码为特殊流形上的点，例如，作为Grassmann、Stiefel以及FLAG流形上的表示。在这种情况下，将开发用于计算描述性统计的算法。Karcher提出了一个计算Grassmann流形上一组点的平均值的算法，这是一个著名的例子。研究人员主要致力于开发具有改进的Grassmannians计算特性的新算法，以及可以应用于例如Stiefel和FLAG流形的算法。这些算法将被设计为实时应用于非常大的数据集，并将使用国防威胁减少局提供的时间演变的高光谱数据集进行评估。这些包括(但不限于)使用法布里-珀罗涉仪和频率捷变激光雷达获取的数据。拟议的跨学科研究计划解决了与国家安全相关的主要挑战，即根据观测数据实时识别和评估环境中的化学和生物风险。提出了用于探索海量化学和生物高光谱数据的新的数学工具，以辅助威胁检测和表征。该研究计划的一个主要目标是应用这些工具，以超过目前用于生物和化学威胁分类的技术的性能能力。预计这一研究计划的结果将对其他与国家安全有关的应用有用，例如检测高光谱图像以外的数据中的异常。