How can separate the correlated parameter estimated by matlab from matrix correlation

Hello

I would like to know how I can decorrelate the parameter estimated from the covariance matrix or coorp

Thank you

Answer 1

[Hari]

Hi yousef swesi,

I understand that you are looking to decorrelate parameters estimated from a covariance matrix or correlation matrix in MATLAB. This process involves transforming the correlated parameters into a set of uncorrelated parameters.

I assume you have a covariance or correlation matrix available from your data or parameter estimation process. You can follow below steps to Decorrelate Parameters:

1. Eigenvalue Decomposition: Perform eigenvalue decomposition on the covariance or correlation matrix. This decomposition separates the matrix into eigenvalues and eigenvectors.
2. Use of Eigenvectors: The eigenvectors represent directions of maximum variance and are orthogonal, meaning they can serve as a new basis for your parameters that are uncorrelated.
3. Transformation: Transform your original correlated parameters using the eigenvectors. This step essentially rotates your parameter space to align with the directions of maximum variance indicated by the eigenvectors.

Example Code:

% Assuming 'C' is your covariance or correlation matrix
[eigVec, eigVal] = eig(C);
% Decorrelate parameters
% Assuming 'params' is a matrix of your parameters, where each row is a parameter and each column is an observation
decorrelatedParams = eigVec' * params;

1. Eigen Decomposition: "eigVec, eigVal = eig(C);" decomposes the covariance or correlation matrix C into its eigenvectors ("eigVec") and eigenvalues ("eigVal").
2. Decorrelation: "decorrelatedParams = eigVec' * params;" transforms the parameters using the transpose of the eigenvectors, resulting in a new set of parameters that are decorrelated.

References:

• For eigenvalue decomposition, refer to the documentation of "eig:" https://www.mathworks.com/help/matlab/ref/eig.html.
• For understanding covariance and correlation matrices, see: https://www.mathworks.com/help/matlab/ref/cov.html for covariance and https://www.mathworks.com/help/matlab/ref/corrcoef.html for correlation.

Hope this helps!