Kernels Flashcards
1
Q
What is a kernel?
A
A Kernels is a function of two original vectors (x, y) that computes the dot product of the expansion of those vectors according to a certain basis function without ever having to compute the actual expansion.
2
Q
Why are kernels useful?
A
This reduces the amount of computation required which increases speed of calcualtions.
3
Q
What is the kernel for polynomials?
A
k(x,y) = (1 + x^Ty)^s
4
Q
What is the kernel for Gaussian?
A
k(x,y) = exp(-||x-y||^2 / 2σ)
5
Q
What is the kernel for sigmoid?
A
k(x,y) = tanh(Kx^Ty - δ)
6
Q
How do we apply kernels to maximisation of L(λ)?
A
max L(λ) = ∑(n=1)^N λ_n - 0.5 ∑(n=1)^N ∑_(m=1)^N (λ_n λ_m t_n t_m k(x_n,x_m))
