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Uniform Convergence of Adaptive Graph-Based Regularization

  • Matthias Hein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4005)

Abstract

The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hölder functions. As an intermediate step we derive upper bounds on the covering numbers of Hölder functions on compact Riemannian manifolds, which are of independent interest for the theoretical analysis of manifold-based learning methods.

Keywords

Riemannian Manifold Uniform Convergence Spectral Cluster Compact Riemannian Manifold Neighborhood Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthias Hein
    • 1
  1. 1.Max Planck Institute for Biological CyberneticsTübingenGermany

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