Writing an optimization code for a function in stform

Hi,

I have a function in stform that translated a regular set of values described by vectors (Xn, Yn) to some measured set (Xr, Yr).

The function was obtained by

st=tpaps([Xn';Yn'],[Xr';Yr'],1);

Each variable is a one column variable. After applying this function on new measurements there are still some systematic errors between the measured values and the values we get from the function. I tried to minimize those errors using an optimization steepest descent algorithm but I have failed. Mainly because the stform doesn't support higher order derivatives and is hard to change. Do you have any suggestion in that respect. The main reason for using the stform is to be able to control the smoothing parameter later on

Answer 1

[Raunak Gupta]

Hi,

In my understanding you are trying to learn a function that has good map between a regular set and a measured set. The tpaps function that is used itself minimize the error between the regular set value and the measured set value. I suggest choosing different ‘p’ values to get even lower systematic error that is there. Since the stform is linear combination of radial basis functions and only small orders polynomial it is not possible to calculate higher order derivative.

Even if you want to minimize the systematic error, I suggest using other curve fitting techniques mentioned here. You may find some Limitations of smoothing spline here helpful for choosing any other curve fitting method.