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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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

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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.

Gamma of an RBF Kernel in SVM

Which of the following would be the best choice for the next RBF SVM you train?

The Radial Basis Function (RBF) kernel is primarily used in Support Vector Machines (SVM) when the dataset is linearly inseparable. The classification performance of an RBF kernel SVM is highly sensitive to its hyperparameters: the regularization parameter $$C$$ and the kernel parameter $$\gamma$$. These hyperparameters are typically tuned using cross-validation on the training data. An RBF kernel SVM is particularly effective when the number of features is relatively small and the number of training samples is moderate.

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