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Sensitivity analysis of Principal Component coefficients

Hi All,

Thank you for provide UQLab. :slightly_smiling_face:

I am using real data and through pca routine from Matlab I have retain 2 principal components and I have 8 variables. For example, one equation maybe: Y1=aX1+bX2+…hX8.
Now, I would like to perform sensitivity analysis for each equation. However, I am not able to do it using UQLab . Can somebody help me?

Best regards,

EFerreira

Hi @EFerreira

It is quite hard to understand where exactly your issue is. Could you possibly elaborate a bit, or ideally share a minimal working example?

Hi @paulremo

Thank you once again for your support.

In the following zip folder, I have put all the files for a short example of what I have done.
pca_analysis is the main file to run. It calls 3 input files and merge them, then I perform Principal Component Analysis for this complete database.
The results are displayed in PCA-output.txt
At the end, I open it and start to see what is the percentagem of total explained variability retaining only 2 components, because I only want to display the results in 2D plot. Then retaining the first two columns of loadings I am able to write the model equations.
For example:
Y1=0.4385var1+0.3980var2+0.3389var3+0.0890var4+0.4887var5+0.4513var6+0.2898*var7
A reviewer kindly suggest me that it would be very interesting to perform Sobol’s indices analysis to the dataset.
It is a completly new area of knowledge for me and through my understanting I think I have to perform global sensitivity of the indices of PC1 and PC2 for each analysis. Maybe, I am wrong. Still I was not able to do it.

I hope I could explain my issue.

Sincerely,

EFerreira

example_PCA_files.zip (5.7 KB)