How to calculate the covariance and correlation among variables and principal components.

When i was doing the PCA analysis, i wanna calculate the covariance and correlations among variables and principal components to see which variables are important based on this correlation matrix?

I don't know how to do that.

Answer 1

[Amish]

Hi Huan,

I see that you want to perform a PCA analysis and calculate the covariance and correlations among principal components.

This can be performed using existing functionalities in-built in the MATLAB. Here is a generic example (using a random sample set) highlighting how you can do the same:

% Example Data
X = randn(100, 5); 
X_standardized = zscore(X);

% PCA
[coeff, score, latent, ~, explained] = pca(X_standardized);

% Covariance and Correlation with PCs
covMatrix = cov(X_standardized);
corrMatrix = corr(X_standardized);
correlationWithPCs = coeff .* sqrt(latent)';

disp('Covariance Matrix:');
disp(covMatrix);
disp('Correlation Matrix:');
disp(corrMatrix);
disp('Correlation with Principal Components:');
disp(correlationWithPCs);

The documentation for the functions mentioned in the above sample can be referred to using the 'doc' command or through the following links:

pca: https://www.mathworks.com/help/stats/pca.html

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

cov: https://www.mathworks.com/help/stats/cov.html

Hope this helps!