If parameter y in the radial kernel K (c, , a,) = exp (y (x, - x,)' )is very large, then "if unsure, try fitting our (or your own) simulated 2D datasets with radial kernels using different gamma and see what happens (use plot() to visualize the separating curve). Or simply plot a graph of K vs c - ; at different values of y O the kernel is non-zero only for extremely close pairs of points and the classifier becomes very "local" and flexible (at the price of potentially having very large variance): a small local vicinity of each point "makes its own prediction". In the limit, each point is fitted independently and the separating curve will "hug" every data point; full separation of the outcome labels can be achieved (but will likely represent a case of heavy overfitting) O the kernel becomes poorly defined. It is not possible to fit SVM with very large 'gamma' the kernel is very "smooth": every prediction is made by averaging the contributions of data points over very large distances (in the original space). The resulting classifier will not be very flexible and will likely have larger bias (will probably not be able to draw a separating curve that's too jagged), but the variance is likely reasonably small (as many points contribute to each prediction, those predictions are expected to generalize well) O the kernel becomes equivalent to a linear kernel. The classifier will thus become just the support vector classifier: it will work well for linearly separable (or nearly separable) datasets