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The Word Mover's Distance (WMD) proposed by Kusner et al. is a distancebetween documents that takes advantage of semantic relations among words thatare captured by their embeddings. This distance proved to be quite effective,obtaining state-of-art error rates for classification tasks, but is alsoimpracticable for large collections/documents due to its computationalcomplexity. For circumventing this problem, variants of WMD have been proposed.Among them, Relaxed Word Mover's Distance (RWMD) is one of the most successfuldue to its simplicity, effectiveness, and also because of its fastimplementations.  Relying on assumptions that are supported by empirical properties of thedistances between embeddings, we propose an approach to speed up both WMD andRWMD. Experiments over 10 datasets suggest that our approach leads to asignificant speed-up in document classification tasks while maintaining thesame error rates.

Speeding up Word Mover's Distance and its variants via properties of distances between embeddings