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I have 4 standard normal features on which I perform PCA. I then take the first principal component (with all of the components). Is it possible to a priori say what is the max and the min value that the transformed series will have?

I guess, if we assume that the original standard normal features never exceed +/- 5, then the max of the final transformed series would be the PCA coefficients product summed by 5? But is it possible that the PCA coefficients are [1, 1, 1, 1] in this case? Or is there some sort of a bound on what the PCA coefficients can be?

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The short answer is that you can determine the max and min of your transformed series if you normalize after your PCA step, as your title implies.

Have you tried L2-norm after your PCA step? This might get you what you are looking for by constraining the values between 0 and 1.

You can, of course, customize this to suit your needs.

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  • $\begingroup$ what do you mean by L2-norm after my PCA? $\endgroup$
    – Naz
    Jan 29, 2019 at 21:39
  • $\begingroup$ It's has multiple names I suppose. It's basically a euclidean distance vector norm: 1. Wolfram 2. Wikipedia If you are interested, you could look at techniques like non-negative matrix factorization (NNMF), which constrains matrix elements to positive-only values. $\endgroup$
    – ngopal
    Feb 7, 2019 at 1:04

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