To deal with negative values, we propose clipped $\mathit {PMI}$,

which is equivalent to $\mathit {PPMI}$ when $z = 0$. In practice we find this works poorly if done symmetrically, so we introduce a variant called $\mathit {NNEGPMI}$ which only normalizes $\mathit {\texttt {-}PMI}$: 
 Question: What novel PMI variants are introduced?
clipped PMI; NNEGPMI