Research Area 3: Mathematical Sciences: 3.4, Discrete Mathematics and Computer Science

Abstract

Many modern applications require modeling and analysis of functions on large, high dimensional, unstructured data sets. One may assume that the data lies on a low dimensional manifold, but this manifold is not known. We have extended the diffusion geometry paradigm for these problems to study function approximation on data defined manifolds. Our algorithms are applied successfully to recognition of hand written digits, classification and missing data problems, automatic diagnosis of age related macular disease based on multi--spectral images, and prediction of blood glucose levels. The ideas are applied to other problems, such as analysis of terrain data and solutions of partial differential equations. The scientific barriers include the development of kernel based methods so as to avoid computation of eigenvalues and eigenvectors of large matrices, and quadrature formulas which are guaranteed to work better than the straightforward Monte Carlo integration method.

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Document Details

Document Type
Technical Report
Publication Date
Jun 10, 2015
Accession Number
ADA625542

Entities

People

  • Hrushikesh N. Mhaskar

Organizations

  • California State University, Los Angeles

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computational Science
  • Computations
  • Computer Science
  • Data Sets
  • Differential Equations
  • Eigenvectors
  • Engineering
  • Equations
  • Geometry
  • Image Processing
  • Mathematics
  • Partial Differential Equations
  • Signal Processing
  • Students
  • Supervised Machine Learning

Fields of Study

  • Computer science

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Neural Network Machine Learning.