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From: Steven on 15 Apr 2010 14:49
Hi,

I'm having a problem where I have 4 parameters that can fit my data. However, these parameters are somehow related to 6 variables that I can control. If I compile lots of data of how the 4 parameters vary with these 6 variables, is there an efficient way in MATLAB to derive some empirical relationship between these values?

Is there a scientific field that focuses on this parameterization problem? It seems like something that would involve functionals or something complicated like that, but I'm not a mathematician. Any direction would be helpful.
From: ImageAnalyst on 15 Apr 2010 16:07
On Apr 15, 2:49 pm, "Steven " <shimiz...(a)gmail.com> wrote:
> Hi,
>
> I'm having a problem where I have 4 parameters that can fit my data. However, these parameters are somehow related to 6 variables that I can control.. If I compile lots of data of how the 4 parameters vary with these 6 variables, is there an efficient way in MATLAB to derive some empirical relationship between these values?
>
> Is there a scientific field that focuses on this parameterization problem? It seems like something that would involve functionals or something complicated like that, but I'm not a mathematician. Any direction would be helpful.

------------------------------------------------------------------------------------
Maybe Principal Components Analysis???
From: Rune Allnor on 15 Apr 2010 16:07
On 15 apr, 20:49, "Steven " <shimiz...(a)gmail.com> wrote:
> Hi,
>
> I'm having a problem where I have 4 parameters that can fit my data. However, these parameters are somehow related to 6 variables that I can control.. If I compile lots of data of how the 4 parameters vary with these 6 variables, is there an efficient way in MATLAB to derive some empirical relationship between these values?
>
> Is there a scientific field that focuses on this parameterization problem? It seems like something that would involve functionals or something complicated like that, but I'm not a mathematician. Any direction would be helpful.

This sounds like a classic least mean squares problem.

The theory is a bit involved as it - as you correctly
expected - relies on vector space analysis. But at the
end of the day everything you need is embedded in the
PINV function. The hard part is to understand what PINV
does and how to interpret the results.

Rune
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