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If I use a manifold learning method to project some data points into a low dimensional space, what will be the distances between the projected points? Can I use Euclidean distance? If the distances will not be Euclidean, what kind of distance metric do I have to use and how?

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It would depend on the manifold learning technique, I think.

DrLIM, for instance is Euclidean, but I've seen other metrics. Section 6 of this paper used cosine distance, and I've seen Hamming distance as well.

Which method did you have in mind?

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  • $\begingroup$ I wanted to use aaai.org/ocs/index.php/AAAI/AAAI10/paper/view/1924. $\endgroup$ – Hossein Abedi Apr 27 '13 at 19:05
  • $\begingroup$ @Hossein Equation 2 seems to suggest that they're using Euclidean distance, but I'm not sure. $\endgroup$ – David J. Harris Apr 27 '13 at 19:19
  • $\begingroup$ That norm is because of this : "Each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.", -from wikipedia! $\endgroup$ – Hossein Abedi Apr 27 '13 at 19:39

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