Move applicable kernels inside Shift Invariant Class

[jonpsy]

This issue address a part of my broader aim to add various kernel support inside RFF. The foundation of which is, to have kernels which are Shift Invariant. This repository has several such kernels, however, they don't derive from the SIV class. My aim, through a series of PR, is to refactor such classes and subsequently add their support to RFF.

Here's a tentative list of kernels I plan to refactor

• Cauchy Kernel
• Chi2Kernel
• Circular Kernel
• More ...

Since the research is new, not all of the aforementioned kernel would be given RFF support.

I also plan to add new kernels, few of them being:

• AdditiveChi2Kernel: https://scikit-learn.org/stable/modules/kernel_approximation.html#additive-chi-squared-kernel
• Skewed Chi Squared Kernel: https://scikit-learn.org/stable/modules/kernel_approximation.html#skewed-chi-squared-kernel

as they have already been implemented along with their spectral density function inside sklearn repo.

[jonpsy]

@gf712 The repo already has Chi2Kernel, the only difference between AdditiveChi2Kernel and our current implementation is, we take the exponential & divide by width whereas AdditiveChi2 doesn't.

Shogun Chi2Kernel:

Sklearn AdditiveChi2Kernel:
k(x, y) = -Sum [(x - y)^2 / (x + y)]

I was thinking we could assimilate AdditiveChi2Kernel inside Chi2Kernel, and user could choose the one the wish to use using some SG parameter. Or would you rather suggest I create a new class?

[stale]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.

[stale]

This issue is now being closed due to a lack of activity. Feel free to reopen it.