Accession Number:

ADA551287

Title:

Diffuse Interface Models on Graphs for Classification of High Dimensional Data

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

2011-01-01

Pagination or Media Count:

30.0

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 edgeregion 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.

Subject Categories:

  • Theoretical Mathematics
  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE