FeatureExtract function with "StandardizedVector" do not show the standard devaition of one

Questions
, ,
1

I am wondering what kind of scaling is applied to the FeatureExtract function with “StandardizedVector” option. The output does not show the standard devaition of one for each columns. This function is used in NetEncoder[“FeatureExtractor”] also.

x={{1., 2., 3.}, {4., 5., 6.}, {7., 8., 9.}, {10., 11., 12.}, {13., 14.,15.}} 

xS01 = FeatureExtract[x, "StandardizedVector"];
xS02 = Standardize[x];
StandardDeviation /@ {xS01, xS02}
Mean /@ {xS01, xS02} // Chop
{{1.11803, 1.11803, 1.11803}, {1., 1., 1.}}

Thanks.

FeatureExtractor_V1.nb (12.1 KB)

2

It uses the biased estimator for the variance

x = {{1., 2., 3.}, {4., 5., 6.}, {7., 8., 9.}, {10., 11., 
   12.}, {13., 14., 15.}}

xS01 = FeatureExtract[x, "StandardizedVector"];
xS02 = Standardize[x];
xS03 = Sqrt[Length[x]/(Length[x] - 1)] xS02;
StandardDeviation /@ {xS01, xS02, xS03}
Mean /@ {xS01, xS02, xS03} // Chop

(*
 {{1., 2., 3.}, {4., 5., 6.}, {7., 8., 9.}, {10., 11., 12.}, {13., 14., 15.}}

 {{1.11803, 1.11803, 1.11803}, {1., 1., 1.}, {1.11803, 1.11803, 1.11803}}

  {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}
*)
3

Thank you for clarification. Could you please provide few references? I am not aware of this biased estimator for the variance.