How to do correlation between each row of two matrices?

I'm trying to calculation the correlation between each individual value in each row to the corresponding row in another matrix.

I have two matrices; both same size 442x1, 442x1.

I used the following code:

DR_all_stv = 442x1 matrix

Participation_Coeff = 442x1 matrix

stv_correlation = (corr(DR_all_stv(1:442,:),Participation_Coeff(1:442,:),'all',')');

However the corresponding code just gives me one correlation value, but I want to create an array that contains a value for each correlation between each row. It should be a 1 to 1 correlation.

Does anyone have any adivce on how I can calculate each correlation between the two corresponding rows?

[Ameer Hamza]

Rows of DR_all_stv and Participation_Coeff have only one element. How do you want to calculate corr() between two scalars? Correlation is defined for multiple data points.

Answer 1

[Tommy]

The default correlation coefficient which corr calculates is described here (the Pearson linear correlation coefficient):

https://www.mathworks.com/help/stats/corr.html#d120e195813

Wikipedia gives a nice alternative formula:

As Ameer implied, plugging scalar values into these equations will result in NaN. Sure enough,

>> corr(rand, rand)

ans =

   NaN

What you can do is calculate a sliding window correlation between signals X and Y where the correlation between X(i) and Y(i) is really the correlation between windows of X and Y which are centered at i. This answer lays it out nicely. For example:

X = DR_all_stv;
Y = Participation_Coeff;
windowSize = 10; % result depends on window size you choose
% e.g. window size of 1 => eX = X, eY = Y, etc => corr is all NaN

eX = movmean(X, windowSize);     % E[X], i.e. eX(i) is E[X(i-windowSize/2:i+windowSize/2)] 
eXX = movmean(X.^2, windowSize); % E[X^2]
eY = movmean(Y, windowSize);     % E[Y]
eYY = movmean(Y.^2, windowSize); % E[Y^2]
eXY = movmean(X.*Y, windowSize); % E[XY]

num = eXY - eX.*eY;
denom = sqrt(eXX - eX.^2) .* sqrt(eYY - eY.^2);
corr = num./denom;