how to do whitening transformation of sum of squared error in matlab in matlab

To perform the whitening transformation of the sum of squared error in MATLAB, you can follow these steps:

1. Load your data into MATLAB as a vector or matrix, depending on your specific scenario.
2. Calculate the mean of your data using the mean function. Let's suppose your data is stored in a variable called data.

main.m
data_mean = mean(data);
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3. Subtract the mean from each data point to center the data around zero.

main.m
centered_data = data - data_mean;
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4. Calculate the covariance matrix of the centered data using the cov function.

main.m
covariance_matrix = cov(centered_data);
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5. Calculate the eigenvectors and eigenvalues of the covariance matrix using the eig function.

main.m
[eigenvectors, eigenvalues] = eig(covariance_matrix);
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6. Sort the eigenvalues and corresponding eigenvectors in descending order.

main.m
[eigenvalues_sorted, indices] = sort(diag(eigenvalues), 'descend');
eigenvectors_sorted = eigenvectors(:, indices);
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7. Compute the whitening matrix by taking the square root of the inverse of the sorted eigenvalues and multiplying it by the sorted eigenvectors.

main.m
whitening_matrix = sqrt(inv(diag(eigenvalues_sorted))) * eigenvectors_sorted';
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8. Apply the whitening transformation to your centered data by multiplying it with the whitening matrix.

main.m
whitened_data = whitening_matrix * centered_data;
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At this point, whitened_data will contain the whitened version of your original data, where the sum of squared error has been transformed by the whitening process.

Note that this process assumes that your data is already properly preprocessed, such as removing any outliers or normalizing it to a consistent scale if necessary.