Finding data with transformation applied

Is there a way to find relatedness between data and the data obtained after some transformation applied to it? i.e. given a data I need to find the most related data(most of the values in that data can be obtained) that can be found by applying some transformation in original data.

I tried but couldn't find a proper answer, most of the discussion that I found is about linear transformation or log transformation but I want to find a way to quantify the relatedness given any transformation.

Thanks!