Longxiu Huang
Michigan State University, MI·Mathematics & Statistics
Modern science produces huge data sets with many dimensions at once: video, medical scans, traffic sensor records, images taken at hundreds of light wavelengths. These data are often noisy, incomplete or partly corrupted, and standard tools struggle at this scale.
- Fields
Mathematics & Statistics
Computer Science
- Topics
tensor data analysis
tensor decomposition
low-rank tensor
- Grants
- 1 known grant, through Jun 2029
What they work on
- Develop mode-wise sampling methods that analyze large tensors (multidimensional data arrays) by working with small slices along each dimension, and prove that this sampling reliably captures the full data.
- Design non-convex optimization and randomized numerical algorithms that recover low-rank structure from incomplete or corrupted tensor data, and establish convergence analysis and perturbation bounds for them.
- Validate the robust tensor framework in computational studies of traffic anomaly detection and of hyperspectral images, which record many wavelengths of light, measuring efficiency and robustness in high-dimensional settings.
More about the research
A natural way to store such data is a tensor, a multidimensional array that extends a matrix to three or more directions and keeps the relationships between those directions intact. This project builds fast, reliable mathematical methods for analyzing very large tensors, and it proves that those methods work.
Why it matters
Fast, provably reliable ways to clean up and analyze huge, corrupted multidimensional data sets could help in medical imaging, national security and other artificial intelligence applications. Concrete test cases include spotting unusual events in traffic data and analyzing hyperspectral images. Scientists and engineers would gain scalable tools that come with mathematical guarantees about how well they work.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
HanQin Cai
University of Central Florida, FL·Mathematics & Statistics
Develop scalable tensor algorithms based on mode-wise sampling and low-rank tensor representations to recover useful information from large, partially corrupted or incomplete multidimensional data.
Anna Ma
University of California-Irvine, CA·Mathematics & Statistics
Analyze the sample complexity of low-rank tensor completion, meaning how many observed entries are needed to recover a multi-dimensional dataset with simple underlying structure.
Fabian Faulstich
Rensselaer Polytechnic Institute, NY·Mathematics & Statistics·Early-career
Recast periodic coupled-cluster theory as a nonlinear Petrov–Galerkin method for a pseudo-differential operator on a high-dimensional torus, in order to derive sharp error estimates for electronic-structure simulations of crystalline materials.
The school
Michigan State University: 28 labs on PI Pages, $932M a year on research, 555 research doctorates a year.
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