Feature Scaling for Positive Features

One of the labs mentioned that scaling features by dividing by the max value works only for positive features. Why is that?

The reason is that dividing by max produces inconsistent scales for negative values whose absolute values are greater than max. This is because dividing by max does not take into account the negative sign.

Hello @mvrbiguv,

Try to think of some examples. If we have only two features of only positive values:

x1 = [1, 3, 5,]
x2 = [2, 4, 10,]

then dividing them by their maximum values will leave us normalized features both with a range of 0 to 1. However, if feature x1 has some negative values:

x1 = [-1000000000, 1, 3, 5]
x2 = [2, 4, 10]

then dividing them by their maximum will NOT give us similar ranges in the two normalized features. Having similar ranges is the purpose for normalization, and that’s why!

Cheers,
Raymond

I see, I thought we were dividing by the maximum absolute value (1000000000 for x1 in the second example). I guess that wouldn’t work either because the normalized values will be between -1 and 1 but the purpose of normalization is to bring values in the range 0 to 1. Or would -1 to 1 work?

I see, I thought we were dividing by the maximum absolute value. I guess that wouldn’t work either because the normalized values will be between -1 and 1 but the purpose of normalization is to bring values in the range 0 to 1. Or would -1 to 1 work?

Both ranges, 0 to 1 and -1 to 1, are valid for normalization.