Collaborative Research: ATD: Theory and Algorithms for Discrete Curvatures on Network Data from Human Mobility and Monitoring

合作研究：ATD：人体移动和监测网络数据离散曲率的理论和算法

• 批准号: 1737812
• 负责人: Jie Gao
• 金额: $ 10万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1737812&HistoricalAwards=false
• 关键词: Collaborative; Research; ATD; Theory; Algorithms

New developments in technologies of embedded systems, sensors, and wireless communications provide great potential to improve the safety and security of the physical and social environment we live in. These technologies can help identify and mitigate unfortunate accidents, emergency events, and malicious attacks. This project seeks to develop mathematical tools and algorithms based on discrete curvatures for the purpose of understanding and detecting community structures and anomalies in networks that can be of crucial value in many applications. The project considers high level mobility patterns, community structures, and anomalies as well as finer details such as who is where. The mathematical tools to be developed will be useful in other networks (for example, protein-protein interactions in biological networks). This project will investigate mathematical problems arising the analysis of real-time spatial and temporal human mobility data. The focus will be on the community detection problem on graphs by using discrete Ricci curvatures and discrete curvature flows on graphs. The problem is to extract stable groups in human mobility patterns, which will serve as the traffic norm for detecting abnormal patterns that can be tied to criminal or terroristic events. To detect these stable groups, or communities, the main observation is that community structures in a network resemble well known geometric phenomena such as thick-thin decompositions in Riemannian geometry. Inspired by Riemannian geometry and the success of Hamilton-Perelman's Ricci flow program, this work investigates how to use discrete curvatures and discrete curvature flows to detect community structure in a network. Preliminary investigations show that the proposed method has great potential and can detect communities with high accuracy. This potential prompts PIs to examine computationally feasible definitions of discrete Ricci curvatures on weighted networks. The important work of Ollivier on discrete Ricci curvature is the starting point of this investigation. The drawback of Ollivier's curvature is that it is computationally expensive -- almost impossible to compute the proposed discrete curvature flow on large networks containing more than a million nodes. As such, the main task in this work is to find computationally feasible Ricci curvatures where the discrete curvature flow can be computed in real time for large networks. The affirmative resolution of this work will be useful in pure mathematical research and computer science. The work will also develop software for practical use.

嵌入式系统，传感器和无线通信技术的新发展为改善我们所生活的物理和社会环境的安全性提供了巨大的潜力。这些技术可以帮助识别和减轻不幸的事故，紧急事件和恶意攻击。该项目旨在基于离散曲率开发数学工具和算法，以理解和检测网络中社区结构和异常情况，这在许多应用程序中可能具有至关重要的价值。该项目考虑了高水平的移动性模式，社区结构和异常，以及更细节的细节，例如谁在哪里。 要开发的数学工具将在其他网络中很有用（例如，在生物网络中的蛋白质 - 蛋白质相互作用）。该项目将研究实时空间和时间人类流动性数据分析的数学问题。 通过使用离散的RICCI曲率和图形上的离散曲率流，将重点放在图形上的社区检测问题上。 问题是要提取人类流动模式的稳定群体，这将作为检测可能与犯罪或恐怖事件相关的异常模式的交通规范。为了检测这些稳定的群体或社区，主要观察结果是网络中的社区结构类似于众所周知的几何现象，例如riemannian几何形状中的厚实分解。受Riemannian几何形状的启发以及汉密尔顿 - 佩雷尔曼（Hamilton-Perelman）的RICCI流程计划的成功，这项工作研究了如何使用离散的曲率和离散曲率流以检测网络中的社区结构。 初步研究表明，该提出的方法具有巨大的潜力，并且可以高精度地检测社区。 这种潜在提示PI检查加权网络上离散RICCI曲率的计算可行定义。 Ollivier在离散RICCI曲率上的重要工作是这项研究的起点。 Ollivier曲率的缺点是它在计算上很昂贵 - 几乎不可能计算包含超过一百万个节点的大型网络上提出的离散曲率流。 因此，这项工作的主要任务是找到计算上可行的RICCI曲率，在这些曲率上可以实时计算离散曲率流量的大型网络。这项工作的肯定分辨率将在纯数学研究和计算机科学中有用。 这项工作还将开发用于实际使用的软件。

项目成果

A Geometric Understanding of Deep Learning

对深度学习的几何理解

• DOI: 10.1016/j.eng.2019.09.010
• 发表时间: 2020-03-01
• 期刊: ENGINEERING
• 影响因子: 12.8
• 作者: Lei, Na;An, Dongsheng;Gu, Xianfeng
• 通讯作者: Gu, Xianfeng

AE-OT-GAN: Training GANs from data specific latent distribution

• DOI: 10.1007/978-3-030-58574-7_33
• 发表时间: 2020-01
• 期刊: ArXiv
• 作者: Dongsheng An;Yang Guo;Min Zhang;Xin Qi;Na Lei;S. Yau;X. Gu

Ae-OT: a New Generative Model based on Extended Semi-discrete Optimal transport

• 发表时间: 2020-04
• 作者: Dongsheng An;Yang Guo;Na Lei;Zhongxuan Luo;S. Yau;X. Gu

Modeling the Space of Point Landmark Constrained Diffeomorphisms

• DOI: 10.1007/978-3-030-58577-8_22
• 发表时间: 2020-08
• 作者: Chengfeng Wen;Yang Guo;X. Gu

Automatic and Robust Skull Registration Based on Discrete Uniformization

• DOI: 10.1109/iccv.2019.00052
• 发表时间: 2019-10
• 期刊: 2019 IEEE/CVF International Conference on Computer Vision (ICCV)
• 作者: Junli Zhao;Xin Qi;Chengfeng Wen;Na Lei;X. Gu