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If one has data that's assumed to be normal distributed and want to use it as input in a machine learning model, why not first standardize the data and then normalize (min max scale it between zero and one)?

So first transform as follows

$$ S = \frac{X - \mu}{\sigma} $$

...and then transform it one more time to $$ X_{standaardizedAndNormalized} = \frac{S - S_{min}}{S_{max}-S_{min}} $$

user3607022
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1 Answers1

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That is equivalent to normalizing only $X$ since the standardization step does not change the min/max values. Besides, these transformations are not associated with normality assumption.

gunes
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    Indeed, an assumption of normality of inputs is rarely a requirement – Sycorax Feb 02 '22 at 22:54
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    If you did the transforms in the opposite order "normalize" then "standardize" you would get the same as just "standardize". Both are location-scale transformations. – Henry Feb 02 '22 at 23:52
  • What's the downside of first standardizing and then normalizing? If there isn't any downside, why not just always do that? – user3607022 Feb 03 '22 at 15:28
  • The first operation is a waste of resources – gunes Feb 03 '22 at 17:42