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

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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.