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Fast Word Mover's Distance Build Status PyPI codecov

Calculates Word Mover's Distance as described in From Word Embeddings To Document Distances by Matt Kusner, Yu Sun, Nicholas Kolkin and Kilian Weinberger.

Word Mover's Distance

The high level logic is written in Python, the low level functions related to linear programming are offloaded to the bundled native extension. The native extension can be built as a generic shared library not related to Python at all. Python 2.7 and older are not supported. The heavy-lifting is done by google/or-tools.


pip3 install wmd

Tested on Linux and macOS.


You should have the embeddings numpy array and the nbow model - that is, every sample is a weighted set of items, and every item is embedded.

import numpy
from wmd import WMD

embeddings = numpy.array([[0.1, 1], [1, 0.1]], dtype=numpy.float32)
nbow = {"first":  ("#1", [0, 1], numpy.array([1.5, 0.5], dtype=numpy.float32)),
        "second": ("#2", [0, 1], numpy.array([0.75, 0.15], dtype=numpy.float32))}
calc = WMD(embeddings, nbow, vocabulary_min=2)
[('second', 0.10606599599123001)]

embeddings must support __getitem__ which returns an item by it's identifier; particularly, numpy.ndarray matches that interface. nbow must be iterable - returns sample identifiers - and support __getitem__ by those identifiers which returns tuples of length 3. The first element is the human-readable name of the sample, the second is an iterable with item identifiers and the third is numpy.ndarray with the corresponding weights. All numpy arrays must be float32. The return format is the list of tuples with sample identifiers and relevancy indices (lower the better).

It is possible to use this package with spaCy:

import spacy
import wmd

nlp = spacy.load('en_core_web_md')
nlp.add_pipe(wmd.WMD.SpacySimilarityHook(nlp), last=True)
doc1 = nlp("Politician speaks to the media in Illinois.")
doc2 = nlp("The president greets the press in Chicago.")

Besides, see another example which finds similar Wikipedia pages.

Building from source

Either build it as a Python package:

pip3 install git+

or use CMake:

git clone --recursive
cmake -D CMAKE_BUILD_TYPE=Release .
make -j

Please note the --recursive flag for git clone. This project uses source{d}'s fork of google/or-tools as the git submodule.


Tests are in and use the stock unittest package.


cd doc
make html

The files are in doc/doxyhtml and doc/html directories.


...are welcome! See CONTRIBUTING and code of conduct.


Apache 2.0

README {#ignore_this_doxygen_anchor}