Spark MLLib's Word2Vec cosine similarity greater than 1

Question

http://spark.apache.org/docs/latest/mllib-feature-extraction.html#word2vec

On the spark implementation of word2vec, when the number of iterations or data partitions are greater than one, for some reason, the cosine similarity is greater than 1.

In my knowledge, cosine similarity should always be about -1 < cos < 1. Does anyone know why?

Answer 1

In findSynonyms method of word2vec, it does not calculate cosine similarity v1・vi / |v1| |vi|, instead it calculates v1・vi / |vi|, where v1 is the vector of the query word and vi is the vector of the candidate words. That's why the value sometimes exceeds 1. Just to find closer words, it is not necessary to divide by |v1| because it is constant.