is it a good idea to take the derivative or integral of some features and add them as new features in machine learning?

Question

I'm learning how to do feature Engineering and come across some ideas in my head that's why I want to ask if I had some dataset with some features let's say 2 features and I have a timestamp column and the dataset is a time series dataset so they are monotonic. would it make sense to calculate the derivative or integral and add it as new feature ?

as an example let's say I have speed and acceleration as features, would it make sense to add the jerk (which is the derivative of the acceleration) and the snap(which is the derivative of the jerk) as new features ? also maybe the integral of the speed which would give the displacement I think?

the goal is let's say 2 features are not enough and we want to produce more features, is it wise to add the derivative or integral as a new feature? or is it a bad idea?

I also want to know whether the correlation between the derivative and integral according to timestamp and the feature that I derivated from would be high if I do this and is it bad or good if I make new features that correlate with others in my dataset

Answer 1

While performing feature engineering , transforming the existing features is recommended step instead of adding transformed values of the existing feature into the dataset. Since, if we add these kind of data elements they will be highly correlated with each other and it effects the model performance. If you have less features and cannot create a model, ask for additional data.