Large-scale high-dimensional data sets are becoming ubiquitous in modern society, particularly in the areas of physical, biomedical, and social applications. This three-year NSF award at the University of North Carolina at Chapel Hill (NSF DMS-2152289) and the University of Illinois at Chicago (NSF DMS-2152070) will address the foundational challenges, both computational and theoretical, arising in the analysis of high-dimensional data by leveraging its compressible features.
The FRG investigators will collaborate across the disciplines of mathematical analysis, data science, statistics, and computation, as well as across institutions. The specific goals of this project include:
- Generalizing classical concepts of “compressible” features using ideas from spectral theory, algebraic geometry, energy and optimization, and network interactions.
- Using newly developed compressible features, the FRG team will then design and develop accurate and efficient computational tools for large-scale high-dimensional data sets.
All the work to be done will be aimed at collaborating directly with application domain scientists to enhance the efficacy of the proposed methods. The FRG investigators will also jointly mentor graduate and undergraduate students, who will then have the benefits of training across disciplines and access to a variety of ideas and tools in complementary and integrative research areas.