I thought Friday was a good excuse to do a very basic question, which still makes me wonder. Why do we need the centering part in standard normalization? Assuming normalization means here, centering plus scaling to the standard deviation.

If we want fairness in the influence of the variables, eg distances, scaling has intuitive meaning. But why the centering matters? I have not found a satisfying answer 'in general'. That is, I am putting aside the cases the the actual algorithm requires such centering; I rather wonder whether centering, by itself, has a generic justification which applies to all or many scenarios. I presume such justification exists somewhere, as we all seem to follow the mantra of doing this standard normalization 'by-default'.

Thanks for sharing in advance, and have a great weekend.

  • $\begingroup$ I marked it as a duplicate of several questions, you can probably find a number of other, similar ones. TL;DR is that scaling, centering, normalization, standardization etc. in some cases, for some algorithms, make the problems computationally easier, so it is easier for the algorithm to find good solution. There's no "generic justification" beyond this. Additionally, in some cases centering, or just shifting the variables, could make the parameters of regression easier interpretable. $\endgroup$ – Tim Mar 6 '20 at 23:11