Free Energy Node Embedding via Generalized Skip-gram with Negative Sampling

A widely established set of unsupervised node embedding methods can be interpreted as consisting two distinctive steps: i) the definition a similarity matrix based on graph interest followed by ii) an explicit or implicit factorization such matrix. Inspired this viewpoint, we propose improvements in both steps framework. On one hand, to encode similarities free energy distance, which interpolates between shortest path and commute time distances, thus, providing additional degree flexibility. other method loss function that generalizes skip-gram model with negative sampling arbitrary matrices. Compared factorizations used $\ell _{2}$ loss, proposed better preserve pairs associated higher scores. Moreover, it easily implemented using advanced automatic differentiation toolkits computed efficiently leveraging GPU resources. Node clustering, classification, link prediction experiments real-world datasets demonstrate effectiveness incorporating free-energy-based well compared state-of-the-art alternatives.