Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization

@article{Lafon2006DiffusionMA,
  title={Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization},
  author={St{\'e}phane Lafon and Ann B. Lee},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2006},
  volume={28},
  pages={1393-1403}
}
  • Stéphane Lafon, Ann B. Lee
  • Published in
    IEEE Transactions on Pattern…
    2006
  • Computer Science, Medicine
  • We provide evidence that nonlinear dimensionality reduction, clustering, and data set parameterization can be solved within one and the same framework. The main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise. Our construction, which is based on a Markov random walk on the data, offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high… CONTINUE READING

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