word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings of Structured Data

Vector representations of graphs and relational structures, whether\nhand-crafted feature vectors or learned representations, enable us to apply\nstandard data analysis and machine learning techniques to the structures. A\nwide range of methods for generating such embeddings have been studied in the\nmachine learning and knowledge representation literature. However, vector\nembeddings have received relatively little attention from a theoretical point\nof view.\n Starting with a survey of embedding techniques that have been used in\npractice, in this paper we propose two theoretical approaches that we see as\ncentral for understanding the foundations of vector embeddings. We draw\nconnections between the various approaches and suggest directions for future\nresearch.\n