Kernel matrix normalization

[simonschoelly]

Would it make sense to have a kernel in this package that wraps another kernel and ensures that the matrix is normalized by calculating

$$K'(x, y) = K(x, y) / sqrt(K(x, x), K(y, y))$$

? I think this might be helpful in cases of non-numeric input such as strings or graphs, where one cannot simply normalize the input features. For example, kernels in GraKeL have this option: https://github.com/ysig/GraKeL/blob/3dc692a86a49542de7314c6d904d9d0afee9d196/grakel/kernels/kernel.py#L60.
Although in GraKeL this is done by passing an rgument to the kernel constructor.

Also, here is some paper on that topic: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.2658&rep=rep1&type=pdf

[willtebbutt]

Hi @simonschoelly . I think this could make sense, although I've not come across these kernels before. Maybe @devmotion or @theogf have?

[theogf]

I think I encountered this normalization before as well (in some student project).
This sounds like an easy addition so I would be in favor of adding it.
Something like NormalizedKernel ?

EDIT: I found the paper : https://research.cs.aalto.fi/pml/online-papers/gonen12icml.pdf (Section 6.1)

[willtebbutt]

Seem reasonable to me. @simonschoelly if you fancied opening a PR that implements this, I would be happy to review.

A good starting point would be to look at how we implement ScaledKernel, or one of the other kernels in that directory.

[devmotion]

Fixed by #274.