Nonlocal Estimation of Manifold Structure

@article{Bengio2006NonlocalEO,
  title={Nonlocal Estimation of Manifold Structure},
  author={Yoshua Bengio and Monperrus Martin and H. Larochelle},
  journal={Neural Computation},
  year={2006},
  volume={18},
  pages={2509-2528}
}
We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at the dimension of the true underlying manifold. This observation invites an exploration of nonlocal manifold learning algorithms that attempt to discover shared structure in the tangent planes at different positions. A training criterion for such an algorithm is proposed, and… Expand
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