Normalization (z-transform) formula?

Fred12
Fred12 New Altair Community Member
edited 2024 05 in Community Q&A

hi,

I am a bit confused what the true formula for z-transform normalization in rapidminer is, normally it is         (X-arithmeticMean(X))/std.deviation

 

but what is the standard-deviation formula? one like that:

https://docs.tibco.com/pub/spotfire/6.5.0/doc/html/norm/norm_z_score.htm

or one used in studentizing:

https://de.wikipedia.org/wiki/Studentisierung

 

or sample variance?

https://de.wikipedia.org/wiki/Stichprobenvarianz

 

and what do I use if I don't know the real arithmetic mean of my values X or the probability distribution of my values of X ?

because variance uses Expectation values from X, and its        variance = SUM(p(x)*X)

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Answers

  • MartinLiebig
    MartinLiebig
    Altair Employee

    Fred,

     

    i totally do not get the question. You are doing data mining, so you always work on estimates of it. Thats the difference between Erwartungswert and Mittelwert in german. The only question is wether you correct with the -1 or not.

     

    ~Martin

  • Fred12
    Fred12 New Altair Community Member

    ok then I was getting something wrong ;)

    when do I apply -1 correction, and when not? where is the difference?

  • MartinLiebig
    MartinLiebig
    Altair Employee

    I think the correct way is to use it with -1. That makes it a unbiased estimator (erwartungstreuer schätzer) for the true std. dev.

     

    Makes no difference for high n though.