A potential problem and a magic solution
If we map the input vectors into a very high-dimensional
feature space, surely the task of finding the maximum-
margin separator becomes computationally intractable?
The mathematics is all linear, which is good, but the
vectors have a huge number of components.
So taking the scalar product of two vectors is very
The way to keep things tractable is to use
“the kernel trick”
The kernel trick makes your brain hurt when you first
learn about it, but its actually very simple.