Enhancing Network Embedding with Auxiliary Information: An Explicit Matrix Factorization Perspective

Recent advances in language modeling such as word2vec motivate a number of graph embedding approaches by treating random walk sequences as sentences to encode structural proximity in a graph. However, most of the existing principles of neural graph embedding do not incorporate auxiliary information such as node content flexibly. In this paper we take a matrix factorization perspective of graph embedding which generalizes to structural embedding as well as content embedding in a natural way. For structure embedding, we validate that the matrix we construct and factorize preserves the high-order proximities of the graph. Label information can be further integrated into the matrix via the process of random walk sampling to enhance the quality of embedding. In addition, we generalize the Skip-Gram Negative Sampling model to integrate the content of the graph in a matrix factorization framework. As a consequence, graph embedding can be learned in a unified framework integrating graph structure and node content as well as label information simultaneously. We demonstrate the efficacy of the proposed model with the tasks of semi-supervised node classification and link prediction on a variety of real-world benchmark network datasets.