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.

该提案涉及开发新的几何算法，用于检测和分类空气中的生物剂和化学剂的威胁。 研究人员提出了一个数学框架，该数学框架集中在编码与流过高光谱图像相关的大规模数据集上，例如特殊歧管上的点，例如，作为格拉斯曼（Grassmann），斯蒂芬（Stiefel）和旗帜歧管的表示形式。 在这种情况下，将开发用于计算描述性统计的算法。 Karcher引入了这种算法的一个众所周知的例子，以计算格拉斯曼歧管上一组点的平均值。 研究人员主要涉及开发具有改进的司硕的计算特性的新算法，以及可以应用于Stiefel和Flag歧管的算法。 这些算法将设计为实时应用于非常大的数据集，并将使用临时不断发展的高光谱数据集进行评估。其中包括（但不限于）使用Fabry-Perot干涉仪和频率敏捷激光雷达获得的数据。拟议的跨学科研究计划解决了与国家安全有关的重大挑战，即，从观察数据中实时识别和评估环境中的化学和生物风险。 提出了用于探索大量化学和生物高光谱数据的新数学工具，以帮助威胁检测和表征。研究计划的主要目标是应用这些工具，以超过用于生物和化学威胁分类的当前技术的性能能力。 预计该研究计划的结果将对与国家安全有关的其他应用程序有用，例如在高光谱图像以外的数据中检测异常。