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I am studying how to use Gaussian RBF kernels for mapping 2D data to 3D. In this link: Use Gaussian RBF kernel for mapping of 2D data to 3D, @MaxS provides an answer on this topic, but I can't understand this formula:

$$ \newcommand{\x}{\mathbf{x}} z(\x) = \sum_{i=1}^n\exp\left\{-\frac{||\x-\x_i||^2}{2\gamma^2}\right\} $$

  • If I want to use SVM, is $\x$ the test data?
  • Is $n$ number of training data?
  • Is $\x_i$ one of training data in this formula?
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Yes to 1 and 3. $n$ is the number of support vectors, which is typically less than the number of training instances.

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  • $\begingroup$ thanks,can you explain more it for me? do you mean that after we used SVM, we can define z for our new data? and why can not we use all training data? I really appreciate you for your help. $\endgroup$ – nnp nnp Apr 3 '15 at 18:17
  • $\begingroup$ I search about this and think that because the value of alpha is zero for nsv you said n is number of support vectors,Am I right? $\endgroup$ – nnp nnp Apr 5 '15 at 7:37
  • $\begingroup$ @nnpnnp yes that is right! $\endgroup$ – Marc Claesen Apr 5 '15 at 9:15

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