I have what I think might be a standard machine learning problem but I can't find a clear solution.
I have lots vectors of different dimensions. For each pair of vectors I can compute their similarity. I would like to embed these vectors into Euclidean space of some fixed dimension $d$ in such a way that vectors that are similar under the original measure have small Euclidean distance under the embedding.
This seems to be called similarity metric learning but the wiki doesn't seem to go into any detail about ways to tackle it. I also found some code for metric learning in Python but it seems to tackle a different problem to the one I am interested in.
How can you tackle this similarity learning problem?