Fit a parameter to minimise a correlation between two vectors

Hello,

I'm struggling to figure out how to formulate a fitting problem in Matlab 2017b.

Bassically I run an experimen and it spits out a number, . However, this number is biased by some other parameters, . There is hypothetical correction factor with the following relationship:

where are all values that can be extracted for a given experiment. δ is a common factor which is unknown, but should be the same for all my data.

So, after acquiring a load of data, are all vectors, and I want to find the value of the number, δ, that minimises the corelation between and .

1. Does Matlab have a good method to deal with this?
2. If not, what is the best way to set it up as a minimisation problem?

Any advice would be appreciated!

Thanks!

Answer 1

[Jeff Miller]

% Some fake data to use in testing:
% Presumably you have your own values for these.
nExpts = 10;
C = rand(nExpts,1);
V1 = rand(nExpts,1);
V2 = rand(nExpts,1);
R1 = rand(nExpts,1);
R2 = rand(nExpts,1);
Nraw = rand(nExpts,1);

% Some boundaries on where you think the best delta might lie.
minDelta = -100;
maxDelta = 100;

% This function call will give you the best delta and the low correlation that it produces:
[bestDelta, bestCorr] = findDelta(C,V1,V2,R1,R2,Nraw,minDelta,maxDelta)

% This function does the actual work:
function [bestDelta, bestCorr] = findDelta(C,V1,V2,R1,R2,Nraw,minDelta,maxDelta)
    [bestDelta, bestCorr] = fminbnd(@fCorr,minDelta,maxDelta);
    
    function theCorr = fCorr(tryDelta)
        Ncorrected = C .* (V1 * tryDelta + V2) ./ (V1 .* R1 * tryDelta + V2 .* R2) .* Nraw;
        theCorr = abs(  corr(V1,Ncorrected)  );  % I'm guessing you want the correlation close to zero, not -1
    end
    
end
    

[chris j]

Thanks for this, Jeff. I'll give it a go today and get back to you!

[Jeff Miller]

Hi Chris, Yes, please let me know whether this does what you want.