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This is a theory/good practice question more than a technical one. If samples are being plotted on a PCA projection of gene expression data, I'm wondering whether it is standard (and if so, why) to center and scale the PCs.

The reason I ask is that in this case the variables (genes) are being measured in the same scale, so I don't know if it would be necessary to center/scale data.

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When the gene expression is scaled and centred you reduce the difference between genes.

Imagine you have one gene A that is highly expressed usually and has a standard deviation of 500 units compared to a gene B that is not much expressed and only have a standard deviation of 5.

In the scaled and centred genes both contribute the same because A usually is expressed 10000 and B is usually expressed 100 units. So, for both the standard deviation is 5% of their expression. Meaning that a variation in one is as important as in the other.

If not scaled (and centred) the first gene A will contribute more to the variation than gene B, because the expression variation in absolute numbers is bigger.

Both are used in publications, but I think the scaled and centred is more used, because the first dimension reflects "better" the differences between samples. Of course you can do both and select the one that is better to show what you want.

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  • $\begingroup$ ...on the other hand, if you scale and centre, a gene with expression 100 becomes as relevant as a gene with expression 10000 which may be undesirable. In the past, I followed the reasoning of the OP and opted against scaling and centring and I used log-transformed expression values (TPM or RPKM). Does this make sense? $\endgroup$ – dariober Aug 2 '18 at 9:09
  • $\begingroup$ @dariober The reasoning I use is, if a gene is usually expressed 1000, it needs this high expression to function, while the other doesn't need to be that high. So, why would I give more relevance to a gene because it needs more expression to keep the cell alive? What I want to see in a PCA is the similarities and differences, not if a gene is differentially expressed or not. About which units to use is (I think) another debate, as the normalization applied will change the apparent similarity between samples $\endgroup$ – llrs Aug 2 '18 at 9:33

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