Accession Number:

ADA625542

Title:

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

Descriptive Note:

Final rept. 25 Aug 2009-28 Aug 2013

Corporate Author:

CALIFORNIA STATE UNIV LOS ANGELES

Personal Author(s):

Report Date:

2015-06-10

Pagination or Media Count:

14.0

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.

Subject Categories:

  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE