Is it suitable to change a feature by itself to generate an another feature?

Question

Hi all I would love to hear your answers on this. Lets say I have two variables, voltage and current, in my data set. I could add another feature by squaring current (so as to calculate power).

Is this an example of feature engineering?

Recently I tried to predict on a diameter prediction on asteroids and I took the natural log of some features which worked well.

Can someone provide some insight as to why this may have improved the model's performance?

Answer 1

Sure, that's feature engineering.

If you're fitting a linear model, then you are looking for features that have a linear relationship with the predicted value. If you're predicting, say, the cost per hour of a device consuming current I, then clearly that's directly related to power not current, so $I^2$ is more likely to be useful.

What you want to be careful about is trying a bunch of transformations of the input blindly; it's possible for a small data set that one odd function of an input happens to be predictive in that sample, but doesn't generalize.