# Normalizing continuous features using sigmoid function

Can you use the sigmoid function to normalize continuous features that have no theoretical maximum value but tend to cluster around [-1, 1]?

Although using the sigmoid function would be a non-linear normalization, my intuition is that the deep neural network or machine learning model that I am training would learn that the continuous feature is not linearly normalized, therefore adapting and doing fine. Is this correct? Can the sigmoid function or any other non-linear normalization method (ex. tanh) be used for continuous features?

The description you give is basically what a sigmoid feed-forward neural network does in its hidden layers: find $$a,b$$ so that $$\sigma(x|a,b)$$ minimizes some loss, where $$\sigma$$ is any sigmoid function, for example you could choose $$\sigma(x|a,b)=\tanh(ax+b)$$. Depending on the choice of $$a,b$$, the function could be basically constant at a large value, basically constant at a small value, or approximately linear, or some kind of mix of all three.