Linear SVMs are very powerful. But sometimes the data are not very linear. To this end, we can use the 'kernel trick' to map our data into a higher dimensional space, where it may be linearly separable. Doing this allows us to separate out non-linear classes. See the below example.
If we attempt to separate the below circular-ring shaped classes with a standard linear SVM, we fail.
But if we separate it with a Gaussian-RBF kernel, we can find a linear separator in a higher dimension that works a lot better.
