Hierarchies over Vector Space: Orienting Word and Graph Embeddings

Word and graph embeddings are widely used in deep learning applications. We present a data structure that captures inherent hierarchical properties from an unordered flat embedding space, particularly a sense of direction between pairs of entities. Inspired by the notion of \textit{distributional generality}, our algorithm constructs an arborescence (a directed rooted tree) by inserting nodes in descending order of entity power (e.g., word frequency), pointing each entity to the closest more powerful node as its parent. We evaluate the performance of the resulting tree structures on three tasks: hypernym relation discovery, least-common-ancestor (LCA) discovery among words, and Wikipedia page link recovery. We achieve average 8.98\% and 2.70\% for hypernym and LCA discovery across five languages and 62.76\% accuracy on directed Wiki-page link recovery, with both substantially above baselines. Finally, we investigate the effect of insertion order, the power/similarity trade-off and various power sources to optimize parent selection.