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I have a variable X with values ranging from -150 to 400. All the other variables in my training set are positive so I normalized them to be from 0 to 1, or they’re already binary, or they had a Gaussian distribution so I used StandardScaler.

For this variable X with some negative values, is it important, generally, that I normalize them to -1 to 1 (due to the negative values) rather than 0 to 1?

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In my opinion, it depends on the importance of the meaning of negative sign.

If the sign of the value indicates the direction of the value, then it will be better to retain the negative sign. For example, +1 indicates moving rightward and -1 indicates moving leftward.

In the other hand, if the the negative sign only means it is smaller than 0, it will be fine to normalize them to 0 to 1. For example, the variable recording temperature, negative values only means it is lower than positive values.

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