Collaborative Research: CDS&E: An Efficient and Robust Algorithmic Framework for Large-Scale Tensor Data Analysis: Theory and Applications

Modern scientific and engineering applications generate many multidimensional datasets that arise in artificial intelligence. Extracting reliable information from these data is challenging because the data are often very large, high dimensional, noisy, and partially corrupted. This project develops efficient and robust mathematical and computational tools for large-scale tensor data analysis, where tensors are multidimensional data structures that preserve important relationships across multiple sources and modalities. The research advances the mathematical foundations of scalable data analysis and scientific computing while supporting national priorities in artificial intelligence and advanced computing, with potential benefits for medical imaging and national security applications. The project advances student education and mentorship through the training of two graduate students and research opportunities for undergraduate students in computational mathematics, optimization, and data science. Outreach and educational activities promote participation in STEM and foster pathways to research and technical careers. This project develops new scalable and provably robust tensor algorithms together with rigorous theoretical foundations for large-scale multidimensional data analysis. The research focuses on mode-wise sampling methods, low-rank tensor representations, randomized numerical techniques, and non-convex optimization algorithms for recovering useful information from corrupted or incomplete data. The project establishes mathematical guarantees for the proposed methods, including convergence analysis, perturbation bounds, and sampling reliability, while achieving improved computational efficiency and robustness in high-dimensional and partially corrupted settings. The resulting framework provides scalable and reliable tools for modern scientific data analysis and will be validated through representative computational studies involving traffic anomaly detection and hyperspectral image analysis. 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. NSF Award ID: 2603464 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: HanQin Cai | Institution: The University of Central Florida Board of Trustees, ORLANDO, FL | Award Amount: $199,852 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2603464 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2603464.html