In matrix factorization for universal schema,<cite> Riedel et al. (2013)</cite> construct a sparse binary matrix of size |P| × |R| whose rows are indexed by entity-pairs (a, b) ∈ P and columns by surface form and Freebase relations s ∈ R. Subsequently, generalized PCA (Collins et al., 2001 ) is used to find a rank-k factorization, i.e., with relation factors r ∈ R |R|×k and entity-pair factors p ∈ R |P|×k , the probability of a relation s and two entities a and b is: