# What is embedding? (in the context of dimensionality reduction)

In the context of dimensionality reduction one often uses word embedding, which seems to me a rather technical mathematical term, which rather stands out compared to the rest of the discussion, which in case of PCA, MDS and similar methods is just the basic linear algebra.

Yet, I would rather avoid using/interpreting this term too loosely. So, what embedding really is: the low-dimensional subspace hidden within a bigger one? The projections of the data vectors onto this subspace? The projection operator mapping the higher-dimensional space onto the lower-dimensional one, as suggested here and here? Something else?

Thank you for clarifications and examples.

• @Tim Thank you. In principle, I have now my question answered. However my formulation is different from those given elsewhere (is embedding a subspace OR a projection OR and operation/function), so you might consider reopening it for the benefit of the community. – Vadim Sep 15 at 8:58