Random Positive-Only Projections: PPMI-Enabled Incremental Semantic Space Construction

We introduce positive-only projection (PoP), a new algorithm for constructing semantic spaces and word embeddings. The PoP method employs random projections. Hence, it is highly scalable and computationally efficient. In contrast to previous methods that use random projection matrices R with the expected value of 0 (i.e., E(R) = 0), the proposed method uses R with E(R) > 0. We use Kendall’s τb correlation to compute vector similarities in the resulting non-Gaussian spaces. Most importantly, since E(R) > 0, weighting methods such as positive pointwise mutual information (PPMI) can be applied to PoP-constructed spaces after their construction for efficiently transferring PoP embeddings onto spaces that are discriminative for semantic similarity assessments. Our PoP-constructed models, combined with PPMI, achieve an average score of 0.75 in the MEN relatedness test, which is comparable to results obtained by state-of-the-art algorithms.