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Highdimensional manifold reconstruction

  1. Sep 6, 2011 #1
    Suppose I have a highdimensional space [itex]\mathbb{R}^N[/itex] that is sparesely populated by a finite set of samples [itex]\{ \mathbf{x} \}_{1 \le i \le k} [/itex], for example N = 500, k = 100. I assume the points x to be sampled from a n-manifold embedded in [itex]\mathbb{R}^N[/itex], where [itex]n << N[/itex]. From a mathematical point of view, would it be legitimate to reconstruct the manifold between samples, e.g. by interpolating the points Hessians? I am aware that therefore the Nyquist criterion must be fulfilled.

    Thanks in advance
  2. jcsd
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