Nonlocal Estimation of Manifold Structure

by Yoshua Bengio, Martin Monperrus and Hugo Larochelle
Abstract: 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 suggests to explore non-local manifold learning algorithms which attempt to discover shared structure in the tangent planes at different positions. A criterion for such an algorithm is proposed and experiments estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms: it is able to generalize very far from training data (on learning handwritten character image rotations), where a local non-parametric method fails.
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Yoshua Bengio, Martin Monperrus and Hugo Larochelle, "Nonlocal Estimation of Manifold Structure", Neural Computation, Massachusetts Institute of Technology Press (MIT Press), vol. 18, no. 10, pp. 2509-2528, 2006.
https://doi.org/10.1162/neco.2006.18.10.2509
Nonlocal Estimation of Manifold Structure
https://hal.archives-ouvertes.fr/hal-01575345/file/Non_Local_Estimation_of_Manifold_Structure.pdf
[Nonlocal Estimation of Manifold Structure](https://hal.archives-ouvertes.fr/hal-01575345/file/Non_Local_Estimation_of_Manifold_Structure.pdf) ([doi:10.1162/neco.2006.18.10.2509](https://doi.org/10.1162/neco.2006.18.10.2509))
\href{https://hal.archives-ouvertes.fr/hal-01575345/file/Non_Local_Estimation_of_Manifold_Structure.pdf}{Nonlocal Estimation of Manifold Structure} % \cite{bengio:hal-01575345}

Bibtex Entry:

@article{bengio:hal-01575345,
 title = {Nonlocal Estimation of Manifold Structure},
 author = {Bengio, Yoshua and Monperrus, Martin and Larochelle, Hugo},
 url = {https://hal.archives-ouvertes.fr/hal-01575345/file/Non_Local_Estimation_of_Manifold_Structure.pdf},
 journal = {{Neural Computation}},
 publisher = {{Massachusetts Institute of Technology Press (MIT Press)}},
 volume = {18},
 number = {10},
 pages = {2509-2528},
 year = {2006},
 doi = {10.1162/neco.2006.18.10.2509},
}
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