Locally Learning Biomedical Data Using Diffusion Frames

Abstract

Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline our mathematical foundations for learning a function on high-dimension biomedical data in a local fashion from training data. Our approach is based on a localized summation kernel, and we verify the computational performance by means of exact approximation rates. After these theoretical results, we apply our scheme to learn early disease stages in standard and new biomedical datasets.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2012
Accession Number
ADA585675

Entities

People

  • F. Filbir
  • H. N. Mhaskar
  • M. Ehler

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Engineered Resilient Systems

DTIC Thesaurus Topics

  • Algorithms
  • Bioengineering
  • Computational Science
  • Computer Programs
  • Data Sets
  • Dimensionality Reduction
  • Disease Attributes
  • Equations
  • Geometry
  • Information Processing
  • Information Science
  • Machine Learning
  • Mathematics
  • Medical Personnel
  • Retinal Diseases
  • Standards
  • Supervised Machine Learning

Fields of Study

  • Computer science

Readers

  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Neural Network Machine Learning.

Technology Areas

  • Biotechnology