Learning Eigenfunctions Links Spectral Embedding and Kernel PCA

@article{Bengio2004LearningEL,
  title={Learning Eigenfunctions Links Spectral Embedding and Kernel PCA},
  author={Yoshua Bengio and Olivier Delalleau and Nicolas Le Roux and Jean-François Paiement and Pascal Vincent and Marie Ouimet},
  journal={Neural Computation},
  year={2004},
  volume={16},
  pages={2197-2219}
}
In this letter, we show a direct relation between spectral embedding methods and kernel principal components analysis and how both are special cases of a more general learning problem: learning the principal eigenfunctions of an operator defined from a kernel and the unknown data-generating density. Whereas spectral embedding methods provided only coordinates for the training points, the analysis justifies a simple extension to out-of-sample examples (the Nystrm formula) for multidimensional… CONTINUE READING
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Random matrix approximation of spectra of integral

  • V. Koltchinskii, E. Giné
  • operators. Bernoulli,
  • 2000
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Random matrix approximation of spectra of integral operators

  • V. Koltchinskii, E. Giné
  • Bernoulli
  • 2000
Highly Influential
2 Excerpts

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