ATD: Landscape Networks and Nonlinear Diffusions for Anomaly Detection and Active Learning

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Statistical and machine learning are revolutionizing scientific fields ranging from computer vision, to medicine, to natural language processing, and inference of natural physical laws. Despite these rapid and impressive empirical advances, machine learning remains only partially understood mathematically. In particular, unsupervised anomaly detection in which algorithms must distinguish background from anomaly with no labeled data and active learning in which only a very small but carefully selected number of points may be queried for labels are ripe for transformational advances. As sensors generate ever increasing datasets, the sheer volume of data overwhelms human capacity for generating the kinds of large training sets necessary for traditional supervised learning algorithms. The future of machine learning relies on developing new mathematical approaches to unsupervised and active learning, where no or little training data is required. Innovations in this direction have potential to transform fields as diverse as computational medicine, network security, and image processing. This project will support 1 graduate student in the second and third years of the grant.This research project develops new algorithms for anomaly detection and active learning in spatiotemporal data. The emphasis is on the analysis of high-dimensional, time-evolving data sets in a manner that is robust to nonlinear geometries, variable sampling rates, and large quantities of noise and outliers. The PI proposes two distinct but related lines of research. First, to devise multitemporal anomaly detection algorithms using landscape cluster networks. This approach handles temporally varying distributions and labels clusters and anomalies at different levels of granularity, providing confidence estimates and uncertainty quantifications. Second, diffusion geometric active learning algorithms for spatiotemporal data will be developed to allow a human analyst to label a small number of queries from the algorithm. These queries are carefully chosen, and the labels provided by the human analyst can radically improve cluster and anomaly detection at minimal computational burden. The proposed methods are robust to complicated data geometries, temporal sampling rates, noise and outliers, and ambient dimensionality of the data. Beyond the topics of machine learning, this project makes broader contributions to probability theory, harmonic analysis, spectral graph theory, high-dimensional statistics, and computational linear algebra. Mathematical and algorithmic contributions will be developed in parallel with scientific collaborations analyzing large spatiotemporal datasets. This project focuses on anomaly detection and active learning in three distinct spatiotemporal data settings: large-scale commuting networks, hyperspectral image analysis, and high energy particle physics. The proposed methods allow for real-time anomaly and threat detection, are scalable, and mitigate the need for large training sets.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.