Data Standardization vs Normalization vs Robust Scaler

Question

I am working on data preprocessing and want to compare the benefits of Data Standardization vs Normalization vs Robust Scaler practically.

In theory, the guidelines are:

Advantages:

1. Standardization: scales features such that the distribution is centered around 0, with a standard deviation of 1.
2. Normalization: shrinks the range such that the range is now between 0 and 1 (or -1 to 1 if there are negative values).
3. Robust Scaler: similar to normalization but it instead uses the interquartile range, so that it is robust to outliers.

Disadvantages:

1. Standardization: not good if the data is not normally distributed (i.e. no Gaussian Distribution).
2. Normalization: get influenced heavily by outliers (i.e. extreme values).
3. Robust Scaler: doesn't take the median into account and only focuses on the parts where the bulk data is.

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I created 20 random numerical inputs and tried the above-mentioned methods (numbers in red color represent the outliers):

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I noticed that -indeed- the Normalization got affected negatively by the outliers and the change scale between the new values became tiny (all values almost identical -6 digits after the decimal point- 0.000000x) even there is noticeable differences between the original inputs!

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My questions are:

1. Am I right to say that also Standardization gets affected negatively by the extreme values as well? If not, why according to the result provided?
2. I really can't see how the Robust Scaler improved the data because I still have extreme values in the resulted data set? Any simple complete interpretation?

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P.S

I am imagining a scenario that I want to prepare my dataset for a Neural Network and I am concerned about the vanishing gradient problem. Nevertheless, my questions are still in general.

Answer 1

Am I right to say that also Standardization gets affected negatively by the extreme values as well?

Indeed you are; the scikit-learn docs themselves clearly warn for such a case:

However, when data contains outliers, StandardScaler can often be mislead. In such cases, it is better to use a scaler that is robust against outliers.

More or less, the same holds true for the MinMaxScaler as well.

I really can't see how the Robust Scaler improved the data because I still have extreme values in the resulted data set? Any simple -complete interpretation?

Robust does not mean immune, or invulnerable, and the purpose of scaling is not to "remove" outliers and extreme values - this is a separate task with its own methodologies; this is again clearly mentioned in the relevant scikit-learn docs:

RobustScaler

[...] Note that the outliers themselves are still present in the transformed data. If a separate outlier clipping is desirable, a non-linear transformation is required (see below).

where the "see below" refers to the QuantileTransformer and quantile_transform.