  Learning good quality neural graph embeddings has long been achieved by
minimizing the point-wise mutual information (PMI) for co-occurring nodes in
simulated random walks. This design choice has been mostly popularized by the
direct application of the highly-successful word embedding algorithm word2vec
to predicting the formation of new links in social, co-citation, and biological
networks. However, such a skeuomorphic design of graph embedding methods
entails a truncation of information coming from pairs of nodes with low PMI. To
circumvent this issue, we propose an improved approach to learning low-rank
factorization embeddings that incorporate information from such unlikely pairs
of nodes and show that it can improve the link prediction performance of
baseline methods from 1.2% to 24.2%. Based on our results and observations we
outline further steps that could improve the design of next graph embedding
algorithms that are based on matrix factorization.
