Why does word2Vec use cosine similarity?

Question

I have been reading the papers on Word2Vec (e.g. this one), and I think I understand training the vectors to maximize the probability of other words found in the same contexts.

However, I do not understand why cosine is the correct measure of word similarity. Cosine similarity says that two vectors point in the same direction, but they could have different magnitudes.

For example, cosine similarity makes sense comparing bag-of-words for documents. Two documents might be of different length, but have similar distributions of words.

Why not, say, Euclidean distance?

Can anyone one explain why cosine similarity works for word2Vec?

Answer 1

Cosine similarity of two n-dimensional vectors A and B is defined as:

which simply is the cosine of the angle between A and B.

while the Euclidean distance is defined as

Now think about the distance of two random elements of the vector space. For the cosine distance, the maximum distance is 1 as the range of cos is [-1, 1].

However, for the euclidean distance this can be any non-negative value.

When the dimension n gets bigger, two randomly chosen points have a cosine distance which gets closer and closer to 90°, whereas points in the unit-cube of R^n have an euclidean distance of roughly 0.41 (n)^0.5 (source)

TL;DR

cosine distance is better for vectors in a high-dimensional space because of the curse of dimensionality. (I'm not absolutely sure about it, though)