Node Embedding based on the Free Energy Distance

We propose a novel unsupervised node embedding method leveraging the free energy distance. More precisely, we build a matrix to encode pairwise node similarities based on the free energy distance, which interpolates between the shortest path distance and the commute time distance, thus providing an additional degree of flexibility. Moreover, we propose a method to factorize the constructed similarity matrix by generalizing the loss function of the skip-gram model with negative sampling to arbitrary similarity matrices. The proposed matrix factorization method can be easily implemented using advanced automatic differentiation toolkits and computed efficiently by leveraging GPU resources. Numerical experiments on four real-world datasets demonstrate that the proposed embedding method outperforms five state-of-the-art alternatives in tasks of node classification and link prediction.