What are some "data transformation" methods? There's a tag here called "data-transformation" described as

Mathematical re-expression, often nonlinear, of data values. Data are
often transformed either to meet the assumptions of a statistical
model or to make the results of an analysis more interpretable.

Could someone run off a list of data transformation techniques, denoting which are linear or non-linear, for me to confirm what I think data-transformation means? Is it only about the transformation of raw data into an alternative form? (but wouldn't that just be  manipulation of what exists in reality, thereby creating synthetic (false) data? a philosophical explanation to complement the list could help)
I'm especially interested in those methods that relate to machine learning whose purpose is the enhancement of a model's out-of-sample performance.
I leave the question openly general to get as many leads as possible, but a brief description of where each technique is commonly applied would be helpful too.
 A: The most common types of data transformation are:

*

*log (natural) transformation

*log(10) transformation

*squared transformation (second order polynomial)

*cubic transformation (third order polynomial)

*square root transformation

*cubic root transformation

Among the most important reasons, we may cite:
a) strategy to produce a normal distribution (not needed for regression, since what matters most is the linearity of the residuals)
b) strategy to re-scale values
c) strategy to include polynomial terms so as to improve a given model.
Caveat: some transformations must take in consideration the existence of zero (e.g. logarithm) or negative values (e.g. square root) beforehand.
With regard to Machine Learning, the most common transformations are:
a) normalization (z-score)
b) median normalization (using the difference from the median  - instead of the mean - in the z-score)
c) min-max (select a pattern of distribution within a range, whose limits are the selected minimum and maximum value)
The main reason is to provide a similar scale to different features.
Hopefully that helps.
