A reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional, which means that if two functions in the RKHS are close in norm, then they are also pointwise close.
Questions tagged [reproducing-kernel-hilbert-spaces]
239 questions
0
votes
0 answers
General approach to check if the given function is NOT a valid kernel
In general, for proving that the given kernel function is valid, I try one of the following two approaches:
Check if the gram matrix is Symmetric Postive Semi Definite.
Check if the kernel function can be expressed in terms of other functions by…
Ansh Khurana
- 101
- 1
0
votes
1 answer
Reducing Kernel Hilbert Space: Reproducing property
If the inner product between two functions is the $\int f(x)g(x)dx$ and it's equal to $\int f(x)g(x)dx = f(x)$, what conditions must $g(x)$ satisfy in order for this equality to hold?
0
votes
1 answer
How to prove that the Gram matrix of the Gaussian kernel has full rank?
I'm trying to prove that, given mutually different points $x_1,\dots,x_m$, the Gram matrix $G$ for the Gaussian kernel has $rank(G)=m$. If I can prove that the Gaussian kernel is strictly positive definite I could follow that all eigenvalues…
Conny
- 137
- 1
- 10
0
votes
0 answers
RKHS of a Polynomial Kernel with negative roots
Wikipedia, and actually all books and ressources I could find, define a polynomlial kerenel as:
$$
K: x,y \mapsto (x^Ty + c)^2,
$$
where $c\ge 0$. What happens if $c < 0$? Take the following kernels for example:
$$
\forall x,y \in…
