Second, while the above analysis had been originally applied to the case of word-context joint distributions p(w, c), it is easy to see that the PMI matrix approximation analysis also holds for every Euclidean embedding of a joint distribution p(x, y) of any two given random variables X and Y .
we note that it holds for wordcontext joint distributions p(w, c), where w is a single word, but c represents its entire preceding context, rather than just a single context word, and c is a vector representation of this entire context.