(PCA) How do I find out if principal components (number of significant coefficients) change over time?
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I have an experiement where I am expecting a dimensionality reduction over time. In this experiment there are five phases.
I am interested in finding out if the prinicpal components change throughout these phases (over time).
I would like to test this by running the PCA on each of these phases to see if they differ.
One idea I had was to determine the number of significant coefficients in a principal component. Could someone tell me if and how that is possible?
If anyone has a different idea I would be happy to hear that as well!
William Rose on 3 Jun 2022
If your hypothesis is true, then the percent of variance explained by the first M principal components (where you can choose M=1, 2, 3 or whatever) should increase with time. You can check this easily.
The vector explained has the percent of variance explained by each principal component (PC). Of course these will always add up to 100%, when you include all the components, but the first few PCs will contain a disproportionately large share. If your hypothesis is true, the sum of the first few elements in explained will grow with time.
See the help for pca.