ATD: Algorithms and Geometric Methods for Community and Anomaly Detection and Robust Learning in Complex Networks

ATD：复杂网络中社区和异常检测以及鲁棒学习的算法和几何方法

• 批准号: 2220271
• 负责人: Feng Luo
• 金额: $ 25万
• 依托单位: Rutgers University New Brunswick
• 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: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2220271&HistoricalAwards=false
• 关键词: ATD; Algorithms; Geometric; Methods; Community

Complex networks arise in many natural systems, such as social networks, opinion networks, and biological networks, as well as in engineered systems like communication networks such as the Internet. Detecting communities, that is, clusters of nodes with dense interconnections, is a crucial problem with numerous applications. In real-world complex networks, community structures change over time. Dynamic networks, where nodes and network topology have mutually dependent (co-evolving) dynamics, are actively studied in physics, control theory, and robotics. The primary objectives of this project are to establish mathematical tools and algorithms for community detection, using geometric techniques, and to develop a mathematical model for dynamic networks. The applications of this project include security and threat detection. Some of the research will involve graduate and undergraduate students, and the software developed will be made freely available to other researchers. Communities in networks can be viewed as discrete counterparts of thick-thin decompositions in Riemannian geometry. Drawing inspiration from geometry and the success of Hamilton-Perelman's Ricci flow program, the investigators recently proposed discrete Ricci flows for community detection in networks. Experimental investigations have demonstrated that the proposed method can accurately detect communities. However, several theoretical problems, such as the long-term convergence of the flow, remain open. Resolving these issues will be the main focus of the first project. The second project aims to find models that explain the emergence of communities in social and opinion networks. By considering a social network as a graph with specific attributes at nodes (e.g., opinions) and edges (e.g., tie relations), the investigators plan to understand how opinions influence tie relations and vice versa over an extended period. They also seek to determine if the network will become polarized or decomposed into communities with different opinions. For threat detection, particular emphasis will be placed on identifying small clusters of extreme. Two mathematical models are proposed to monitor the dynamic changes in opinion networks. The main goals are understanding the long-term behavior of these models and mathematically establishing the existence of the asymptotic limit.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.

复杂网络出现在许多自然系统中，例如社交网络、意见网络和生物网络，以及工程系统，例如通信网络，例如互联网。检测社区，即具有密集互连的节点集群，是许多应用的关键问题。在现实世界的复杂网络中，社区结构随着时间的推移而变化。动态网络，其中节点和网络拓扑具有相互依赖（共同进化）的动态，在物理学，控制理论和机器人学中被积极研究。该项目的主要目标是建立数学工具和算法的社区检测，使用几何技术，并开发一个动态网络的数学模型。该项目的应用包括安全和威胁检测。一些研究将涉及研究生和本科生，开发的软件将免费提供给其他研究人员。 网络中的社区可以看作是黎曼几何中粗细分解的离散对应物。从几何学和Hamilton-Perelman的Ricci流程序的成功中汲取灵感，研究人员最近提出了离散Ricci流用于网络中的社区检测。实验研究表明，该方法可以准确地检测社区。然而，一些理论问题，如长期收敛的流量，仍然开放。解决这些问题将是第一个项目的主要重点。第二个项目旨在找到解释社区在社会和舆论网络中出现的模型。通过将社交网络视为在节点处具有特定属性的图（例如，意见）和边缘（例如，领带关系），调查人员计划了解意见如何影响领带关系，反之亦然，在一个较长的时期。他们还试图确定网络是否会两极分化或分解为不同意见的社区。对于威胁探测，将特别强调识别小规模极端威胁集群。提出了两个数学模型来监测意见网络的动态变化。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。