@inproceedings{3213,
  title = {From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians},
  journal = {Proceedings of the 18th Conference on Learning Theory (COLT)},
  abstract = {In the machine learning community it is generally believed that
  graph Laplacians corresponding to a finite sample of data points
  converge to a continuous Laplace operator if the sample size
  increases. Even though this assertion serves as a justification for many
  Laplacian-based algorithms, so far only some aspects of this claim
  have been rigorously proved.  In this paper we close this gap by
  establishing the strong pointwise consistency of a family of
  graph Laplacians with data-dependent weights to some
  weighted Laplace operator. Our investigation also
  includes the important case where the data lies on a submanifold of
  $R^d$.},
  pages = {470-485},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  year = {2005},
  note = {Student Paper Award},
  slug = {3213},
  author = {Hein, M. and Audibert, J. and von Luxburg, U.}
}