I understand from Hinton's paper that T-SNE does a good job in keeping local similarities and a decent job in preserving global structure (clusterization).
However I'm not clear if points appearing closer in a 2D t-sne visualization can be assumed as "more-similar" data-points. I'm using data with 25 features.
As an example, observing the image below, can I assume that blue datapoints are more similar to green ones, specifically to the biggest green-points cluster?. Or, asking differently, is it ok to assume that blue points are more similar to green one in the closest cluster, than to red ones in the other cluster? (disregarding green points in the red-ish cluster)
When observing other examples, such as the ones presented at sci-kit learn Manifold learning it seems right to assume this, but I'm not sure if is correct statistically speaking.
I have calculated the distances from the original dataset manually (the mean pairwise euclidean distance) and the visualization actually represents a proportional spatial distance regarding the dataset. However, I would like to know if this is fairly acceptable to be expected from the original mathematical formulation of t-sne and not mere coincidence.