ATD: Collaborative Research: Inference of Human Dynamics from High-Dimensional Data Streams: Community Discovery and Change Detection

在移动和大数据时代，人类在物理空间和虚拟空间的移动和互动数据无处不在。在大数据分析的帮助下，人类动力学的研究成为一项及时的努力。这项研究的结果有助于理解人类活动如何随着时间的推移而变化，以及它们如何改变环境、经济和政治。在微观尺度上，对社区、影响传播、异常检测和流动性预测的研究可以有利于市场研究、减轻犯罪以及减轻和控制流行病。因此，该项目不仅将推动数学和统计学的发展，还将推动人文地理、商业和公共卫生等许多其他领域的发展。该项目旨在分析大型时空数据集中的多关系数据，涵盖了与人类动力学研究相关的广泛主题，包括异常检测、趋势发现、隐藏社区检测、模式挖掘和角色预测等。数据分析的类型涵盖了图上支持的非结构化数据和结构化数据的统计推断。研究工作包括四个主要方向：1)非平稳时间序列的潜在网络估计；2)高维时间序列的在线变化点检测和同步测试；3)基于张量分解和效度测试的多关系数据分析；4)图信号的空间和频谱分析。这些研究项目不仅有助于时间序列分析、张量分析和图形信号处理，而且有助于从大型时空数据集中进行机器学习。这三个领域和机器学习之间的协同作用为多关系数据建模和挖掘规则和不规则结构上定义的数据提供了强大的方法。这项研究将为时间序列和动态复杂网络以及广泛应用的实用软件工具提供理论基础。该奖项反映了美国国家科学基金会的法定使命，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。

In the mobile and big data era, data on human mobility and interaction in both physical space and virtual space are pervasively available. The study of human dynamics with the assistance of big data analytics becomes a timely effort. The outcome from this study helps understand how human activities change over time and how they may change the environment, economy, and politics. At the micro scale, research on communities, influence propagation, anomaly detection, and mobility prediction can benefit marketing research, mitigate crimes, as well as mitigate and contain epidemics. Therefore, this project will advance not only mathematics and statistics, but also many other fields including human geography, business, and public health. The project aims to analyze multi-relational data in large spatiotemporal datasets, and covers a broad range of topics pertaining to the study of human dynamics, including anomaly detection, trend discovery, hidden community detection, pattern mining, and role prediction, etc. The types of data analysis covers statistical inference on both unstructured data and structured data that are supported on a graph. The work includes four major thrusts: 1) latent network estimation from non-stationary time series, 2) online change-point detection and synchronization testing for high-dimensional time series, 3) multi-relational data analysis based on tensor factorization and validity testing, and 4) spatial and spectral analysis of graph signals. These research projects will contribute to not only time series analysis, tensor analysis, and graph signal processing, but also machine learning from large spatiotemporal datasets. The synergy between the three areas and machine learning enables powerful methodologies for modeling multi-relational data and mining data defined on both regular and irregular structures. This research will result in theoretical foundations underpinning time series and dynamic complex networks as well as practical software tools for a broad range of applications.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.