### Inside Kernels…

Given a point x in the input space, the function k(., x) is essentially function

So, x is mapped into a function space (known as Reproducing kernel Hilbert space (RKHS)

When we measure similarity of two points x and y in the input space, we are actually

measuring the similarity between two functions k(., x) and k(., y) in RKHS. How is this

similarity defined in in RKHS? By a (defined) inner product in RKHS:

Reproducing

property

All the solutions so far we obtained has the form:

This means these solutions are functions in RKHS.

Functions in RKHS are nicer: they are smooth, they have finite-dimensional representation.

Good for computations and practical solutions

See “Learning with kernels” for more; Must read G. Wahba’s work to learn more on RKHS vis-à-vis M/C Learning.