"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.

The TensorFlow docs agree with you. This field has such jargon proliferation, it's hard to keep up.

https://developers.google.com/machine-learning/crash-course/...

Yeah, I agree. The number of new nouns per year is kind of ridiculous.

Projection is a type of embedding. But you can't really describe what LTSA, UMAP, etc. do as projection. LTSA "unrolls" data rather than projecting it.

On the contrary, I'd say an "unrolling" is a non-linear projection. Wikipedia suggests that embedding is a type of projection. I hadn't heard the term before today.

https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduc...

Embedding is the ML term for a non-linear projection.

Amusingly, it seems you and the other reply are contradicting each other, saying both that an embedding is a specific type of projection and that a projection is a specific type of embedding.

When I was learning about SVMs way back when, we said "non-linear projection" instead of "embedding".

I mean both are correct given the literature at this point. Maybe the use of embedding captures the notion that you are mapping through a NN which is a variable function of sorts instead of a single or set of linear or orthonormal functions.

The mathematical term "Embedding" refers to finding a lower dimensional representation of some high(er) dimensional data, whether this is done with single function (maybe hand chosen) or a neural network doesn't matter.

I don't think that's quite right.. According to wikipedia, embedding is: https://en.wikipedia.org/wiki/Embedding

So Projection sounds closer to what you describe. https://en.wikipedia.org/wiki/Projection_(mathematics)

So my original comment is not quite right either. The embedding is a structure preserving map. A projection isn't necessarily structure preserving. ''' To be an embedding, such a mapping must preserve order "both ways": ''' http://mathworld.wolfram.com/Embedding.html

I think that a projection from p dimensions to q<p dimensions isn't structure preserving.

At this point a mathematician may be able to explain more.

SVMs project the data into a higher dimensional space, not lower. A mixed blob of dots on a plane can't be cleanly separated by a line into two colors, but if you blow them out into a cube by some arbitrary projection, a plane will be able to separate them cleanly.