A subtle point not really mentioned or brought out. These vectors are 300 dimensional, and once you perform an "analogy " of "X - Y + Z = W" its almost certain that W does not exactly match anything in your vector space (probability of overlap is almost certainly zero). That means you must have an algorithm for choosing which non-matching word to pick. The point of the article is that if you pick strictly the closest one (in terms of euclidean distance in the space) then you usually end up back where you started. There are many measures that could be used, and who is to say that distance along all dimensions are equally important?
In 3d space for example (much simplified from 300d), things that are separated along a vertical axis are usually very different in kind than things separated even by a great distance on the horizontal axis (100m below you is likely to be much different from 100m in front of you).
Or imagine a sky scraper most of the "sameness" lies in a small horizontal region (one block say), but a vast vertical region (100 stories).
This is a simplified analogy to word vectors, but the point is that because two words are "close" in 300d space, if we don't understand what those dimensions mean, we can't say which one is more likely to be "similar" for a specific pair of words (King/Queen vs Mouse/Cat). Using euclidean or cosine similarity may or may not be relevant for one particular case.
In 3d space for example (much simplified from 300d), things that are separated along a vertical axis are usually very different in kind than things separated even by a great distance on the horizontal axis (100m below you is likely to be much different from 100m in front of you).
Or imagine a sky scraper most of the "sameness" lies in a small horizontal region (one block say), but a vast vertical region (100 stories).
This is a simplified analogy to word vectors, but the point is that because two words are "close" in 300d space, if we don't understand what those dimensions mean, we can't say which one is more likely to be "similar" for a specific pair of words (King/Queen vs Mouse/Cat). Using euclidean or cosine similarity may or may not be relevant for one particular case.