Shall I use the Euclidean Distance or the Cosine Similarity to compute the semantic similarity of two words? I want to compute the semantic similarity of two words using their vector representations (obtained using e.g. word2vec, GloVe, etc.). Shall I use the Euclidean Distance or the Cosine Similarity?

The GloVe website mentions both measures without telling the pros and cons of each:


  The Euclidean distance (or cosine similarity) between two word vectors provides an effective method for measuring the linguistic or semantic similarity of the corresponding words.
First of all, if GloVe gives you normalized unit vectors, then the two calculations are equivalent. In general, I would use the cosine similarity since it removes the effect of document length. For example, a postcard and a full-length book may be about the same topic, but will likely be quite far apart in pure "term frequency" space using the Euclidean distance. They will be right on top of each other in cosine similarity.