Gamma controls how far the influence of a single training example reaches, which in turn affects how tightly the decision boundaries end up surrounding points in the input space.

Small Gamma means a larger similarity radius. So that points farther apart are considered similar, which results in more points being grouped together and smoother decision boundaries.

For larger values of Gamma, the kernel value decays very quickly, and points must be very close to be considered similar. This results in more complex, tightly constrained decision boundaries.

University of Michigan - Ann Arbor

The similarity between two points and the transformed feature space is an exponentially decaying function of the distance between the vectors and the original input space.
$$K(x, x') = e^{-\gamma||x - x'||^2}$$

Using this kernel, the linear decision boundary in the feature space corresponds to a non-linear decision boundary in the original input space.

Radial Basis Function (RBF) Kernel in SVM

Gamma of an RBF Kernel in SVM

After training a Radial Basis Function (RBF) kernel SVM, you decide to increase the influence of each training point and to simplify the decision surface.

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