[xtacy]

Oops, sorry, I didn't mean to say you used a RBF kernel. I edited my comment above. I meant to say your embedding resembles the polynomial kernel (not RBF, which was just meant as a generalisation of such neat tricks :)).

What I meant to say was that you didn't need to compute the embedding explicitly. Since you embed into a space that has a nice structure, you can compute the dot product of the embedded vectors without having to compute the embedding explicitly.