How to use Grey Correlation analysis to obtain correlation coefficient?

Hi everyone.

I have a data matrix with ten columns that I want to find the correlation coefficient of each column of this matrix with the target vector with Grey Correlation Analysis method. Can anyone explain the steps of this algorithm. Please help me. I need your help.

Answer 1

[Image Analyst]

Do you mean like this:

% Get data.
data = rand(10, 10); % 10 columns of data
[rows, columns] = size(data)
targetVector = rand(rows, 1);
% Get correlation coefficients
correlationCoefficients = zeros(1, columns);
for col = 1 : columns
	correlationCoefficientMatrix = corrcoef(data(:, col), targetVector);
	correlationCoefficients(col) = correlationCoefficientMatrix(1, 2)
end

[Nazila Pourhajy]

Thanks for your answer my friend. But I want to get correlation coefficient by GCA(Grey Correlation Analysis).

I found the method algorithm,but I do not know it is right or not?

this is input data matrix:

The step of GCA:

1- Normalize data: find minimum of each column and we normalize each array element by this formula:

2-Then,we obtain a new matrix from subtracting the target vector of each column of input data matrix. we acount Min and Max new matrix element and get another new matrix by this formula:

3-And finally,we get correlation coefficient by this formula:

Does these steps based on these formula correct? Please help me and correct my error. Thanks alot.

[Image Analyst]

I think you can figure this out.

For Step 1 you can use rescale().

For step 2 just use division, subtraction, and multiplication along with min(abs(lambda0-lambdaz)).

For step 3 use the sum() function and division.

I'm not sure what equation (4) is used for. It seems deltaoz is not used anywhere, unless you want to replace the expression in equations (5) and (6) with it.

[Nazila Pourhajy]

My problem is that the correlation coefficient obtained with GCA with coefficients obtained with Copula is not the same in Matlab. I thought that the GCA steps might be wrong.