"Embedding" is the term I've heard used for this most often. It's definitely the term that seems to dominate in the literature. (Just to pick a random paper off my reading list: https://arxiv.org/abs/1709.03856 .)

In my mind "embedding" carries the connotation that you're moving into a smaller space that's easier to work with, and where things which are similar in some way are near each other.