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

Tags

Fields of Study

  • Computer science

Readers

  • Graph Algorithms and Convex Optimization.
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks
  • Space