Modern theory and applications of manifold learning
Abstract
The PI, Dr. Amit Singer, proposes research addressing manifold learning methods. The PI identifies how noisy and missing data have continued as an important problem in artificial intelligence, machine learning and data analytics. The standard assumption is that the input data set lies on or near a dimensional (sub)manifold. The key tasks are dimensionality reduction, function representation and approximation, and semi-supervised learning. Most data analysis methods in this setting rely on pairwise Euclidean distances between the data points in the data set. Here Singer will examine and report on some non-Euclidean methods and metrics, thus greater flexibility is allowed in the data sets, thereby being useful for machine learning in situations, for example, structural biology learning the conformation space of flexible proteins and other macromolecules with continuous variability. This work will leverage randomized numerical linear algebra, random matrix theory, higher order statistics, and diffusion maps with non-Euclidean metrics.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310249
Entities
People
- Amit Singer
Organizations
- Air Force Office of Scientific Research
- Trustees of Princeton University
- United States Air Force