Can I scale a dataset using different methods on different columns and why?

Question

relatively new to this and this question has been plaguing me.

Say I have a dataset with feature A, feature B, and feature C. I need to scale for my model. Based on their distributions, feature A is suited to robust scaling, feature C is suited to standardization and feature B is suited to log transformation. I have been told that it is acceptable to use different scalers or transformations on different features; that it is okay to scale feature A using a robust scaler and then to transform feature B using log transform and to standardize feature C.

If this is indeed okay (and I am not sure), why? It seems a bit counter-intuitive to me- won't this change how the variables relate to one another? I would have assumed (before I was told otherwise) that one scaler had to be applied to each feature to keep the relationships intact.

I would really love a discussion or explanation if at all possible- seeing the math would probably help me too. I know this is very theoretical but it truly is driving me nuts.

Answer 1

This will depend on what you do with the scaled data afterwards. Without knowing this I don't think it's a good idea, as scaling normally should make variables comparable, i.e. "bring them on the same scale". For sure log transformation does something very different from scaling, and if you do that, normally you should still scale afterwards if you want the values to be comparable with those from other scaled variables. Also if you need robustness, better scale all variables robustly; I don't think this will do harm even for variables that don't have outliers. If you scale them differently, you won't achieve comparability in a well defined sense. (Note though that "robust scaling" will not cure your data from potential issues with outliers; it may make outliers lie out even further, compared with other variables.)