I have 2 ensemble for which i would like to mesure their similarity/overlap, but there is no existing method to do this on the type of data contained in these ensemble.
However i can apply a transformation to both of them and obtain two new ensemble for wich there is known similarity metrics.
I would like to argue that if the two resulting sets overlap following an identical transformation, then it is the case for the original sets.
An extreme case would be a null transformation, where any element becomes zero, and disproves the theory.
What kind of restriction do i need to set on the transformation for the conclusion to hold?