What are the main advantages and disadvantages of normalization between 0 and 1 or the other zero mean variance one algorithm? If we want to preprocess the data, how to select either of these two normalization methods?
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1$\begingroup$ What is "the other zero mean variance algorithm"? $\endgroup$– Christoph HanckMar 26, 2015 at 9:09
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1$\begingroup$ Terminology here as elsewhere can be a sheer nuisance. Normalizing as used variously in statistical science can mean (1) scaling by (value $-$ minimum) / (maximum $-$ minimum) (2) scaling by (value $-$ mean) / SD (often called standardization, itself a term with multiple other meanings) (3) occasional variants on (2) with e.g. median and IQR instead (4) transforming to approximate normality (Gaussianity) of distribution. I doubt that is a complete list; regardless, it is almost always advisable to give a formula too for what you discuss. $\endgroup$– Nick CoxMar 26, 2015 at 11:39
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Normalizing all variables to have zero mean and unit variance allows you to have direct interpretation of results of any analysis on those variables, since all of them have the same metrics or measurement orders.
This is normally preferred to normalizing variables to be between zero and one, since this other option is strongly influenced by the presence of outliers.
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1$\begingroup$ Conversely, if it's ever important to have variables with the same range, then the first method is essential and the other will almost certainly not work. (Tautological perhaps, but needed for balance.) $\endgroup$– Nick CoxMar 26, 2015 at 11:41
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$\begingroup$ However, when you are dealing with heavy-tailed/skewed distributions, you can't rely on standardization ($\frac{x-\bar{x}}{\sigma_{x}}$), and maybe you'd prefer a unity-based normalization. Do you agree? $\endgroup$ Mar 26, 2015 at 12:46
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$\begingroup$ It depends,but I would agree with Nick Cox from my experience with different geophysical data sets. $\endgroup$ Mar 26, 2015 at 12:48