@inproceedings{3893,
  title = {Uniform Convergence of Adaptive Graph-Based Regularization},
  journal = {Learning Theory: 19th Annual Conference on Learning Theory (COLT 2006)},
  booktitle = {COLT 2006},
  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 Hoelder functions. As an intermediate
  step we derive upper bounds on the covering numbers of Hoelder functions on
  compact Riemannian manifolds, which are of independent interest
  for the theoretical analysis of manifold-based learning methods.},
  pages = {50-64},
  editors = {Lugosi, G. , H.-U. Simon},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = sep,
  year = {2006},
  slug = {3893},
  author = {Hein, M.},
  month_numeric = {9}
}