If parameter in the radial kernel K ( x i , x j ) = e x p ( ( x i x j ) 2 ) 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 x i x j at different values of 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) the kernel becomes poorly defined. It is not possible to fit SVM with very large 'gamma'. You Answered 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