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

在移动的和大数据时代，关于物理空间和虚拟空间中的人的移动性和交互的数据普遍可用。在大数据分析的帮助下研究人类动力学成为一项及时的努力。这项研究的结果有助于了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。在微观层面上，对社区、影响力传播、异常检测和移动性预测的研究可以有益于营销研究，减少犯罪，以及减轻和遏制流行病。因此，该项目不仅将促进数学和统计学，还将促进人文地理学、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，并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。主要工作包括4个方面：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点检测和同步检验; 3）基于张量分解的多关系数据分析和有效性检验; 4）图形信号的空间和谱分析。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，还有助于从大型时空数据集进行机器学习。这三个领域和机器学习之间的协同作用使强大的方法能够对多关系数据进行建模，并挖掘在规则和不规则结构上定义的数据。这项研究将为时间序列和动态复杂网络提供理论基础，并为广泛的应用提供实用的软件工具。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。

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.