Lets say I have objective functions A, B and C. A is the original (GT supervised) objective function I want to minimize, while B and C are unsupervised alternatives (resulting in the same end-goal).
Now I want to find out if B or C are better in approximating A.
Therefore, I trained my model with A and calculated B and C along the way.
Is it correct to say that the objective function with the higher correlation coefficient to A will also give the best results?