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I have performed PCA on gene expression data having 20,000 genes (these are my variables). All values are positive.

The PC1 scores for some of the patients (out of 1089) are as follows:

-158271.26229      12962.73772   19410.42314  324372.09441
 410186.46224     140222.21492  158159.11682 -224566.35112
-158070.07088     -78099.70606  126694.22508  -74185.23425
  37071.94993    1479125.93204  812833.70820  -85862.15807

My question is, what do these negative values mean?? Note that some other values are positive.

kjetil b halvorsen
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Marwah Soliman
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  • @GeoMatt22 Why do you think it's a duplicate of that question? This seems be asking why the scores of PC1 have positive and negative values. The answer is, I assume, that it's due to centering of all variables prior to PCA. But this is not about switching the sign of the whole PC component. I vote to reopen. – amoeba Apr 30 '17 at 13:18
  • @amoeba I did not look too closely at the linked question, my bad! I had figured all "sign of PCA" questions were already answered somewhere on CV, so just took the first one (which was "why *this* sign?" vs. "why *any* sign?" here). You would be the one to know if this has a duplicate somewhere :) Voted to re-open. (BTW I did not get your ping, not sure why.) – GeoMatt22 Apr 30 '17 at 16:42
  • @GeoMatt22 To be honest, I can only guess what exactly the question is about. But if guessed correctly (see my edits), then it's not a duplicate - at least not a duplicate of that thread. – amoeba Apr 30 '17 at 17:31
  • @amoeba OK. I think sign of PCA scores is never "meaningful" though, no? (perhaps [ZCA](https://stats.stackexchange.com/a/117463/127790) precludes reflections?) So the question title would perhaps be better "Why do I get some negative PCA scores for non-negative data?" (to which "centering" would be an appropriate answer) – GeoMatt22 Apr 30 '17 at 17:53
  • @GeoMatt22 Edited. – amoeba Apr 30 '17 at 18:22
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    so is the answer because the negative scores tend to have greater values of variables with negative loadings?? – Marwah Soliman Apr 30 '17 at 22:00
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    It's conventional to report PC scores with mean zero. Therefore, negative scores are those below the mean. What are you reading to understand PCA? – Nick Cox Mar 03 '20 at 07:27
  • https://stats.stackexchange.com/questions/222/what-are-principal-component-scores https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/2698 – kjetil b halvorsen Dec 05 '20 at 12:19

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