Explaining Node Embeddings

Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following two questions: (Q1) Can we explain each embedding dimension with human-understandable graph features (e.g. degree, clustering coefficient and PageRank). (Q2) How can we modify existing node embedding algorithms to produce embeddings that can be easily explained by human-understandable graph features? We find that the answer to Q1 is yes and introduce a new framework called XM (short for eXplain eMbedding) to answer Q2. A key aspect of XM involves minimizingthenuclearnormofthegeneratedexplanations. Weshowthatbyminimizingthe nuclear norm, we minimize the lower bound on the entropy of the generated explanations. We test XM on a variety of real-world graphs and show that XM not only preserves the performance of existing node embedding methods, but also enhances their explainability.