I'm currently trying to wrap my head around the t-SNE math. Unfortunately, there is still one question I can't answer satisfactorily: What is the actual meaning of the axes in a t-SNE graph? If I were to give a presentation on this topic or include it in any publication: How would I label the axes appropriately?
P.S: I read this Reddit question but the answers given there (such as "it depends on interpretation and domain knowledge"), don't really help me to understand this.
Individual axes in t-SNE have no meaning at all.
Algorithms such as MDS, SNE, t-SNE, etc. only care about pairwise distances between points. They try to position the points on a plane such that the pairwise distances between them would minimize a certain criterion. This means that if you take a t-SNE plot and rotate it, then the resulting arrangement will be equally good as far as t-SNE is concerned. So the overall rotation that you get out of t-SNE algorithm is arbitrary.
To label the axes, I recommend writing something like "t-SNE dimension 1" and "t-SNE dimension 2".
(Sometimes people write "t-SNE 1" and "t-SNE 2" or some such, which is sloppy. Sometimes I see "t-SNE component 1" and "t-SNE component 2"; but I think that the word "component" does not work very well in this context.)