word2vec Explained: deriving Mikolov et al.'s negative-sampling word-embedding method
This is an incremental clarification for researchers and practitioners struggling to understand the word2vec methodology.
The paper explains the derivation of the negative-sampling method in Mikolov et al.'s word2vec, which provides state-of-the-art word embeddings, by clarifying cryptic equations from the original research.
The word2vec software of Tomas Mikolov and colleagues (https://code.google.com/p/word2vec/ ) has gained a lot of traction lately, and provides state-of-the-art word embeddings. The learning models behind the software are described in two research papers. We found the description of the models in these papers to be somewhat cryptic and hard to follow. While the motivations and presentation may be obvious to the neural-networks language-modeling crowd, we had to struggle quite a bit to figure out the rationale behind the equations. This note is an attempt to explain equation (4) (negative sampling) in "Distributed Representations of Words and Phrases and their Compositionality" by Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Corrado and Jeffrey Dean.