Regularization on graphs with function-adapted diffusion processes

Published

Journal Article

Harmonic analysis and diffusion on discrete data has been shown to lead to state-of-the-art algorithms for machine learning tasks, especially in the context of semi-supervised and transductive learning. The success of these algorithms rests on the assumption that the function(s) to be studied (learned, interpolated, etc.) are smooth with respect to the geometry of the data. In this paper we present a method for modifying the given geometry so the function(s) to be studied are smoother with respect to the modified geometry, and thus more amenable to treatment using harmonic analysis methods. Among the many possible applications, we consider the problems of image denoising and transductive classification. In both settings, our approach improves on standard diffusion based methods.

Cited Authors

  • Szlam, AD; Maggioni, M; Coifman, RR

Published Date

  • August 1, 2008

Published In

Volume / Issue

  • 9 /

Start / End Page

  • 1711 - 1739

Electronic International Standard Serial Number (EISSN)

  • 1533-7928

International Standard Serial Number (ISSN)

  • 1532-4435

Citation Source

  • Scopus