question: rbf-interpolation out of range about mathtoolbox

[yuki-koyama]

Hi,

with linear kernel they grow to infinity, with gaussian kernel they fade to 0

This is true, and this is known as a limitation of RBF interpolation (and many other interpolation techniques) --- interpolation techniques are simply not good at extrapolation.

I'd be happy if value computed 'outside' matched nearest sample or close to that

In one-dimensional cases, it is easy to achieve this by inserting some if statements before calling RBF interpolation. E.g., if x is larger than x_max (in data) or smaller than x_min (in data), then return f(x_max) or f(x_min).

If the dimensionality is 2 or more, then it is not very trivial. However, there are some mathematical techniques that can be used here (e.g., [*]). This is not yet implemented in this library, unfortunately.

[*]: Section 3.1: Radial basis function with polynomial term https://dl.acm.org/doi/10.1145/2614028.2615425

[shekh]

Thanks for replying, well at least I got a confirmation that it is not simple (need multiple dimensions).

[yuki-koyama]

Note that the latest version provides an option (enabled by default) about using "polynomial term", and it provides better extrapolation behavior.