Multi-parametric regression in MATLAB?

Question

I have a curve which looks roughly / qualitative like the curves displayed in those 3 images.

The only thing I know is that the first part of the curve is hardware-specific supposed to be a linear curve and the second part is some sort of logarithmic part (might be a combination of two logarithmic curves), i.e. linlog camera. But I couldn't tell the mathematic structure of the equation, e.g. wether it looks like a*log(b)+c or a*(log(c+b))^2 etc. Is there a way to best fit/find out a good regression for this type of curve and is there a certain way to do this specifically in MATLAB? :-) I've got the student version, i.e. all toolboxes etc.

Answer 1

fminsearch is a very general way to find best-fit parameters once you have decided on a parametric equation. And the optimization toolbox has a range of more-sophisticated ways.

Comparing the merits of one parametric equation against another, however, is a deep topic. The main thing to be aware of is that you can always tweak the equation, adding another term or parameter or whatever, and get a better fit in terms of lower sum-squared-error or whatever other goodness-of-fit metric you decide is appropriate. That doesn't mean it's a good thing to keep adding parameters: your solution might be becoming overly complex. In the end the most reliable way to compare how well two different parametric models are doing is to cross-validate: optimize the parameters on a subset of the data, and evaluate only on data that the optimization procedure has not yet seen.

Answer 2

You can try the "function finder" on my curve fitting web site zunzun.com and see what it comes up with - it is free. If you have any trouble please email me directly and I'll do my best to help.

James Phillips zunzun@zunzun.com