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I am having difficulty interpreting the shape of the SVM margin.

In both of the following examples, the RBF kernel is used:

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Here the separator is almost the same in the two cases. In the case of the larger gamma (the second example), it is the margin that became more influenced by the shape of the data. What is the significance of these particular training samples at the bottom being support vectors? What is the significance of the samples further at the bottom being inside the margin?

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1 Answers1

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  1. By definition of the radial kernel, when gamma is large, only samples near x give significant terms in the sum in the formula for f(x).
  2. Hence, when gamma is large and x is far from any sample, f(x) is very small.
  3. Margin is a line beyond which f(x) is greater than 1. Given the item 2, it is now clear why the margin has the observed shape when gamma is large.
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