Collaborative Research: ATD: Rapid Structure Recovery and Outlier Detection in Multidimensional Data

合作研究：ATD：多维数据中的快速结构恢复和异常值检测

• 批准号: 2319370
• 负责人: James Wilson
• 金额: $ 14.47万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-09-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2319370&HistoricalAwards=false
• 关键词: Collaborative; Research; ATD; Rapid; Structure

The project aims to develop and apply tools coming from algebra to identify attacks embedded within legitimate communications streams and online fora. The research will enhance statistical methods and Artificial Intelligence to detect and combat threats. Specifically, the research will work with unlabeled data and will be applicable in environments that cannot support learning on training data, such as new domains or previously unseen threats. The project will provide training opportunities for both undergraduate and graduate students, preparing them for their future careers in STEM fields. The research on detecting outliers in data, recovering missing data, and detecting hidden constraints will have many applications across the sciences.The project aims to design a self-adaptive linear-time algorithm to separate signals, find hidden constraint equations, and detect similarities in high-dimensional data (tensors). This collaborative research of the three investigators and student participants will focus on three independent tasks. The first will extend signal separation and outlier prediction to a continuous spectrum. The second will refactor algebraic structures into tensor networks for uniform algorithms. The third will devise faster (linear-time) solutions to matrix systems to enhance practical range. Analysis of high-dimensional data often runs afoul of the curse of dimensionality: as the number of independent parameters increases, the time needed to search neighbors grows exponentially. Also, the meaning of outlier becomes blurred as notions of far apart and close together are less distinguishable, and traditional statistics tend to identify large subspaces. The new algebraic markers will detect structure in any dimension and be quickly computable.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在开发和应用来自代数的工具，以识别嵌入在合法通信流和在线福拉的攻击。该研究将增强统计方法和人工智能，以检测和打击威胁。具体来说，该研究将与未标记的数据一起使用，并且将适用于无法支持在培训数据（例如新领域或以前看不见的威胁）上学习的环境。该项目将为本科生和研究生提供培训机会，为他们在STEM领域的未来职业做准备。关于检测数据中异常值，恢复数据的异常值以及检测隐藏约束的研究将在整个科学中具有许多应用程序。该项目旨在设计一种自适应线性时算法来设计单独的信号，查找隐藏的约束方程，并在高维数据（Tensors）中检测相似之处（Tensors）。这项对三名研究人员和学生参与者的合作研究将集中在三个独立任务上。第一个将将信号分离和离群值扩展到连续频谱。第二个将将代数结构重构为张量网络，以进行均匀算法。第三个将将更快的（线性时间）解决方案设计到矩阵系统以增强实际范围。高维数据的分析通常会因维度的诅咒而出现：随着独立参数的数量增加，搜索邻居所需的时间呈指数增长。同样，由于遥远和近距离的概念较不可分割，离群值的含义变得模糊，而且传统的统计数据倾向于识别大型子空间。新的代数标记将在任何维度上检测结构，并可以快速计算。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响评估标准，被认为值得通过评估来获得支持。