Different influences of outliers on feature scaling: standardization VS. normalization?

by Tyler 提督九门步军巡捕五营统领   Last Updated October 02, 2018 10:19 AM

I've come to know that normalization (MinMax scaling) and standardization (Z-score normalization) on data have different influences from outliers in the data. In About Feature Scaling and Normalization, the author Sebastian Raschka says:

"(Min-Max scaling...) The cost of having this bounded range - in contrast to standardization - is that we will end up with smaller standard deviations, which can suppress the effect of outliers."

In his book Python Machine Learning, 2nd Edition, he mentioned:

"Furthermore, standardization maintains useful information about outliers and makes the algorithm less sensitive to them in contrast to min-max scaling, which scales the data to a limited range of values."

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What does he mean that MinMax scaling can suppress the effect of outliers compared to standardization?

What does he mean that standardization maintains useful information about the outliers and makes algorithm less sensitive to them in contrast to min-max scaling?

Can this be explained from the perspective of the equations?

Standardization: $z=\frac{x-\mu}{\sigma}$

Normalization: $X_{norm}=\frac{X-X_{min}}{X_{max}-X_{min}}$



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