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: 2319371
• 负责人: Martin Kassabov
• 金额: $ 13.88万
• 依托单位: Cornell 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=2319371&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代数工具来识别合法通信流和在线论坛中嵌入的攻击。该研究将增强统计方法和人工智能来检测和对抗威胁。具体来说，该研究将使用未标记的数据，并将适用于无法支持训练数据学习的环境，例如新领域或以前未见过的威胁。该项目将为本科生和研究生提供培训机会，为他们未来在 STEM 领域的职业生涯做好准备。检测数据中的异常值、恢复丢失数据和检测隐藏约束的研究将在整个科学领域有许多应用。该项目旨在设计一种自适应线性时间算法来分离信号、找到隐藏约束方程并检测高维数据（张量）。三名研究人员和学生参与者的合作研究将重点关注三项独立的任务。第一个将信号分离和异常值预测扩展到连续频谱。第二个将代数结构重构为张量网络以实现统一算法。第三个将为矩阵系统设计更快（线性时间）的解决方案，以增强实际范围。高维数据的分析经常会遇到维数灾难：随着独立参数数量的增加，搜索邻居所需的时间呈指数增长。此外，离群值的含义变得模糊，因为远距离和近距离的概念不太容易区分，而传统统计倾向于识别大的子空间。新的代数标记将检测任何维度的结构并可快速计算。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。