Neural graph embeddings via matrix factorization for link prediction: smoothing or truncating negatives?

Learning good quality neural graph embeddings has long been achieved by minimzing the pointwise mutual information (PMI) for co-occuring 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 skeumorphic 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 factorizaion.