# Fit a parameter to minimise a correlation between two vectors

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chris j on 30 Jan 2020
Commented: Jeff Miller on 1 Feb 2020
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?
Thanks!

Jeff Miller on 30 Jan 2020
% 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 on 31 Jan 2020
Thanks for this, Jeff. I'll give it a go today and get back to you!
Jeff Miller on 1 Feb 2020
Hi Chris, Yes, please let me know whether this does what you want.