How to Select Support Vector Machine Kernels

Given an arbitrary dataset, you typically don't know which kernel may work best. I recommend starting with the simplest hypothesis space first -- given that you don't know much about your data -- and work your way up towards the more complex hypothesis spaces. So, the linear kernel works fine if your dataset if linearly separable; however, if your dataset isn't linearly separable, a linear kernel isn't going to cut it (almost in a literal sense;)). For simplicity (and visualization purposes), let's assume our dataset consists of 2 dimensions only. Now, it looks like both linear and RBF kernel SVM would work equally well on this dataset.