# How use logistic function to normalize data to (0,1)

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. When I did some testing computation in Excel I never get value from mentioned interval but every time I get number 1. 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: $$f(x)=\frac{1}{1+e^{-\frac{x}{\alpha}}}$$.

• 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. Nov 5, 2021 at 21:30
• 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
– Ben
Nov 5, 2021 at 22:51