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I am reading paper about data normalization and I am interested how is it possible to use the logistic sigmoid function to normalize data to the specific interval (0,1). There is only short mention in the paper.

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When I did some testing computation in Excel I never get value from mentioned interval but every time I get number 1.

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Excel is rounding to 1. Using the logistic function for normalization would have a narrow domain.

$\lim_{x\rightarrow\infty} \frac{1}{1+e^{-x}}=1$

Even for $x=100$ it's too close to 1: $f(100)\approx0.9999999999999999999999999999999999999999999627992402397916403704...$

You'd be better off with min max normalization, though this is to the range $[0,1]$.

If you needed $(0,1)$, you could squash your logistic function by $\alpha$ like so: $f(x)=\frac{1}{1+e^{-\frac{x}{\alpha}}}$.

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  • $\begingroup$ How could be value of α parameter determined with respect to original values that are normalized in running window? So I do not know min and max value of new observations in dataset. $\endgroup$
    – jnemecz
    Commented Nov 5, 2021 at 21:30
  • $\begingroup$ You wouldn't need an actual min/max, but an estimate. Anything below/above the min/max would be just be closer to 0/1. If you can estimate the min/max then you could probably find a decent $\alpha$. Otherwise, I'm not sure how you'd normalize the data $\endgroup$
    – Ben
    Commented Nov 5, 2021 at 22:51

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