ATD: Detection and Classification of Threats Using Subspace Manifold Geometry

ATD：使用子空间流形几何进行威胁检测和分类

• 批准号: 1322508
• 负责人: Michael Kirby
• 金额: $ 40.16万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1322508&HistoricalAwards=false
• 关键词: ATD; Detection; Classification; Threats; Using

This proposal concerns the development of new mathematical algorithms for detecting and classifying threats in large data sets arising from the presence of, e.g., biological agents or chemical plumes. The investigators propose a geometric framework centered on encoding massive data sets on subspace manifolds. Exploiting the fact that a set of points of a given class can be represented as a low-dimensional subspace of a high dimensional ambient space, it is possible to capture more variability in the threats and thus characterize them with higher accuracy. There are many ways to represent data via subspaces, each leading to a rigorous notion of a manifold, e.g., the Grassmann and Stiefel manifolds. The investigators propose to use the geometry of these manifolds, either as abstract points or via constructing embeddings in Euclidean space, for representing patterns in threats. Detection and classification algorithms originally proposed for vector spaces may now be extended to algorithms over subspace manifolds. The proposed interdisciplinary research program addresses the detection and classification of chemical and biological threats, a major challenge for National Security. Threats delivered to an urban environment or military theater, are potentially comprised of unknown substances and the goal is to detect, characterize and track the threat. Alternatively, threats may be associated with known substances and the goal is to not only detect but classify the actual material or agent by matching it to a library of signatures of known threats. The basic research to be performed will be evaluated in the context of data sets made available by the Defense Threat Reduction Agency. These include (but are not limited to) data acquired using a Fabry-Perot Interferometer, Frequency Agile Lidar, and Raman Spectroscopy. The research will be led by faculty from the Departments of Mathematics and Computer Science at Colorado State University, providing the students with unique multidisciplinary experience with research integration in education.

该建议涉及开发新的数学算法，用于检测和分类大数据集中的威胁，这些威胁来自于，例如，生物制剂或化学羽流研究人员提出了一个以子空间流形上的大量数据集编码为中心的几何框架。利用给定类的一组点可以表示为高维环境空间的低维子空间的事实，可以捕获威胁中的更多变化性，从而以更高的准确度表征它们。有许多方法可以通过子空间表示数据，每种方法都导致流形的严格概念，例如，格拉斯曼和斯蒂费尔流形研究人员建议使用这些流形的几何形状，无论是作为抽象点，还是通过在欧几里得空间中构建嵌入，来表示威胁的模式。最初针对向量空间提出的检测和分类算法现在可以扩展到子空间流形上的算法。拟议的跨学科研究计划解决了化学和生物威胁的检测和分类，这是国家安全的一个重大挑战。交付给城市环境或军事战区的威胁可能由未知物质组成，目标是检测、表征和跟踪威胁。 或者，威胁可能与已知物质相关联，目标是不仅检测实际材料或制剂，而且通过将其与已知威胁的特征库相匹配来对其进行分类。 将根据国防威胁减少局提供的数据集对将要进行的基础研究进行评估。这些包括（但不限于）使用法布里-珀罗干涉仪、频率捷变激光雷达和拉曼光谱学获取的数据。该研究将由科罗拉多州立大学数学和计算机科学系的教师领导，为学生提供独特的多学科经验，并将研究整合到教育中。

项目成果

Subspace Quantization on the Grassmannian

• DOI: 10.1007/978-3-030-19642-4_25
• 发表时间: 2019-04
• 作者: S. Stiverson;M. Kirby;C. Peterson