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For the below code for Mathematica 11.3, I got {-0.153792, 1., 1.} as output.

fe = FeatureExtraction[{{1.4, "A"}, {1.5, "A"}, {2.3, "B"}, {5.4, "B"}}]
fe[{2.4, "A"}]

How can I reconstruct the result of FeatureExtraction manually and obtained {-0.153792, 1., 1.} as output?

Many thanks!

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This can be done by some experiments.

First: There are many automatic options of Mathematica. In Mathematica 11.3 we can get more informations about functions, for example we can do Options[fe] to find out more details.

Let's make things easier.

So we reconstruct a method named "NumericVector" in 1-Dimension[FeatureSpace] data maybe without the effect of DimensionReduction. In high-dimension data maybe done Standardize+PCA[Linear DimensionReduce] by Mathematica.

In your example, A and B are treated as Nominal Feature.

Let's concentrate on the numeric part.

data={{1},{0},{-1}};
fe=FeatureExtraction[data,{"NumericVector"}];
fe@data
Standardize@data
Standardize[data,Mean,.816497&]
{{1.22474},{0.},{-1.22474}}
{{1},{0},{-1}}
{{1.22474},{0.},{-1.22474}}

enter image description here

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