Premise: I have a dataset of elements for which I have a representation in 2 different spaces, a "latent" space and the original space (I can move between those with an Autoencoder neural network).
I want to prove a conjecture where I think that a distance that I developed for the original space doesn't "correlate" with the euclidean distance in the latent space. (By correlate I mean that I feel that "close" elements in one space are "distant" in the other, by their respective distances)
I have computed the distance matrix for both the distances, each in its relative space, for each pair of samples in the dataset.
How do you suggest I can prove this or verify it?