Infinite Dimensions Trick

An SVM using the RBF kernel $K(x,z) = \exp(-\gamma|x-z|^2)$ implicitly maps inputs into a feature space of what dimensionality, and how is the decision boundary computed without ever forming that mapping explicitly?

The same dimensionality as the input space, since RBF only rescales distances rather than transforming features

A dimensionality chosen by cross-validation as a hyperparameter, similar to choosing k in k-NN

Infinite-dimensional feature space; the boundary is computed only through pairwise kernel evaluations (dot products) via the kernel trick, never explicit feature vectors

A fixed finite dimension equal to the number of training points, computed by explicitly building that feature matrix

Infinite-dimensional, but it must be explicitly approximated with a Taylor series truncated to a few terms before training