For this purpose, we also study low-rank embeddings of the PPMI matrix, which allow us to make predictions for unseen pairs.
let m = |{x : (x, y) ∈ P ∨ (y, x) ∈ P}| denote the number of unique terms in P. Furthermore, let X ∈ R m×m be the PPMI matrix with entries M xy = ppmi(x, y) and let M = U ΣV ⊤ be its Singular Value Decomposition (SVD).