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I asked it some time ago: https://cs.stackexchange.com/questions/147713/why-word-embeddings-are-compared-with-cosine-distance-and-not-euclidean https://cs.stack
by estebarb 3y ago
I asked it some time ago: https://cs.stackexchange.com/questions/147713/why-word-embeddings-are-compared-with-cosine-distance-and-not-euclidean https://cs.stackexchange.com/questions/147713/why-word-embed...
There is other aspect: if all vectors are normalized then cosine distance is just dot product. It is faster to calculate than euclidean distance.
- soVeryTired 3y agoI have to say, neither of those answers are very satisfying. Neither is wrong but I don't come away with a clear explanation for why cosine similarity is the obvious metric to use.
- sdenton4 3y agoFor euclidean distance, we have (q-v)^2 = qq + vv - 2qv. The qq and vv don't tell us anything about the relationship between q and v, so are irrelevant to search. So really we are mostly trying to maximize inner product when we search. Additionally, the scale of q (the query) is constant across any given search, so might as well normalize q; the results won't change. Then the only question is whether the scale of v matters... It, again, doesn't tell us anything about the relationship between q and v. So, might as well normalize... And then we are just doing cosine similarity.