Diffuse Interface Models on Graphs for Classification of High Dimensional Data

Abstract

There are currently several communities working on algorithms for classi cation of high dimensional data. This work develops a class of variational algorithms that combine recent ideas from spectral methods on graphs with nonlinear edge/region detection methods traditionally used in in the PDE-based imaging community. The algorithms are based on the Ginzburg-Landau functional which has classical PDE connections to total variation minimization. Convex-splitting algorithms allow us to quickly nd minimizers of the proposed model and take advantage of fast spectral solvers of linear graph-theoretic problems. We present diverse computational examples involving both basic clustering and semi-supervised learning for di erent applications. Case studies include feature identi cation in images, segmentation in social networks, and segmentation of shapes in high dimensional datasets.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2011
Accession Number
ADA551287

Entities

People

  • Andrea Bertozzi
  • Arjuna Flenner

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Classification
  • Clustering
  • Computational Science
  • Data Sets
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Graph Theory
  • Image Processing
  • Image Segmentation
  • Machine Learning
  • Random Walk
  • Semi-Supervised Learning
  • Supervised Machine Learning

Fields of Study

  • Computer science

Readers

  • Distributed Systems and Data Platform Development
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms