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What is the influence of the sigma or gamma parameter for the rbf kernel?

if possible a graph for a better understanding

Is epsilon also known as SIGMA?

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  • $\begingroup$ Good to know that the sigma on rbf is the same as the gamma parameter passed onto SVC $\endgroup$ Dec 29 '19 at 15:04
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The gamma parameter in the RBF kernel determines the reach of a single training instance. If the value of Gamma is low, then every training instance will have a far reach. Conversely, high values of gamma mean that training instances will have a close reach. So, with a high value of gamma, the SVM decision boundary will simply be dependent on just the points that are closest to the decision boundary, effectively ignoring points that are farther away. In comparison, a low value of gamma will result in a decision boundary that will consider points that are further from it. As a result, high values of gamma typically produce highly flexed decision boundaries, and low values of gamma often results in a decision boundary that is more linear.

http://scikit-learn.org/stable/modules/svm.html

https://www.youtube.com/watch?v=m2a2K4lprQw

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I’m here to understand it too, but I’ll post what my book says about this:

The 𝛾 parameter, which we set to gamma=0.1, can be understood as a cut-off parameter for the Gaussian sphere. If we increase the value for 𝛾, we increase the influence or reach of the training examples, which leads to a tighter and bumpier decision boundary

By the way, 𝛾 and σ are equivalents

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