I'm aware that linear transformations of inividual features do not affect Random Forest.

But, what I the same linear transformation to all examples in a dataset to construct a new feature?

I do the following:

I take each sample, i.e. each training example, and linearly combine the features for that training example. The result of this combination is a single value, and this single value becomes another feature for this training example.

For all of the samples, I do the same: Linearly combining all of the values for the features, creating this new feature.

  The resulting data matrix of course has an extra column for this extra feature.

Does this impact the results of a Random Forest?

It is not a linear/monotonic transformation of any one of the features, but rather it is a linear combination of all of the features for a single training example.

I'm aware that linear transformations of individual features do not affect Random Forest.

But what if features were linearly recombined to construct a new feature?

I do the following: I take each sample, i.e. each training example, and linearly combine the features for that training example. The result of this combination is a single value, and this single value becomes another feature for this training example. For all of the samples, I do the same: Linearly combining all of the values for the features, creating this new feature. The resulting data matrix of course has an extra column for this extra feature.

• Does this impact the results of a Random Forest?

• It is not a linear/monotonic transformation of any one of the features, but rather it is a linear combination of all of the features for a single training example.