PyEMD is a Python wrapper for Ofir Pele and Michael Werman's implementation of the Earth Mover's Distance that allows it to be used with NumPy. If you use this code, please cite the papers listed at the end of this document.

This wrapper does not expose the full functionality of the underlying implementation; it can only used be with the np.float data type, and with a symmetric distance matrix that represents a true metric. See the documentation for the original Pele and Werman library for the other options it provides.

To install the latest release:

pip install pyemd

To install the latest development version:

pip install "git+https://github.com/wmayner/pyemd@develop#egg=pyemd"

>>> from pyemd import emd
>>> import numpy as np
>>> first_signature = np.array([0.0, 1.0])
>>> second_signature = np.array([5.0, 3.0])
>>> distance_matrix = np.array([[0.0, 0.5], [0.5, 0.0]])
>>> emd(first_signature, second_signature, distance_matrix)
3.5

You can also get the associated minimum-cost flow:

>>> from pyemd import emd_with_flow
>>> emd_with_flow(first_signature, second_signature, distance_matrix)
(3.5, [[0.0, 0.0], [0.0, 1.0]])

emd(first_signature, second_signature, distance_matrix)

• first_signature: A 1-dimensional numpy array of np.float, of size N.
• second_signature: A 1-dimensional numpy array of np.float, of size N.
• distance_matrix: A 2-dimensional array of np.float, of size NxN. Must be symmetric and represent a metric.

emd, flow = emd_with_flow(first_signature, second_signature, distance_matrix)

• first_signature: A 1-dimensional numpy array of np.float, of size N.
• second_signature: A 1-dimensional numpy array of np.float, of size N.
• distance_matrix: A 2-dimensional array of np.float, of size NxN. Must be symmetric and represent a metric.

• distance_matrix must be symmetric.
• distance_matrix is assumed to represent a true metric. This must be enforced by the user. See the documentation in pyemd/lib/emd_hat.hpp.
• The flow matrix does not contain the flows to/from the extra mass bin.
• The signatures and distance matrix must be numpy arrays of np.float. The original C++ template function can accept any numerical C++ type, but this wrapper only instantiates the template with double (Cython converts np.float to double). If there's demand, I can add support for other types.

To help develop PyEMD, fork the project on GitHub and install the requirements with pip.

The Makefile defines some tasks to help with development:

• default: compile the Cython code into C++ and build the C++ into a Python extension, using the setup.py build command
• build: same as default, but using the cython command
• clean: remove the build directory and the compiled C++ extension
• test: run unit tests with py.test

• All credit for the actual algorithm and implementation goes to Ofir Pele and Michael Werman. See the relevant paper.
• Thanks to the Cython devlopers for making this kind of wrapper relatively easy to write.

Ofir Pele and Michael Werman, "A linear time histogram metric for improved SIFT matching," in Computer Vision - ECCV 2008, Marseille, France, 2008, pp. 495-508.

@INPROCEEDINGS{pele2008,
  title={A linear time histogram metric for improved sift matching},
  author={Pele, Ofir and Werman, Michael},
  booktitle={Computer Vision--ECCV 2008},
  pages={495--508},
  year={2008},
  month={October},
  publisher={Springer}
}

Ofir Pele and Michael Werman, "Fast and robust earth mover's distances," in Proc. 2009 IEEE 12th Int. Conf. on Computer Vision, Kyoto, Japan, 2009, pp. 460-467.

@INPROCEEDINGS{pele2009,
  title={Fast and robust earth mover's distances},
  author={Pele, Ofir and Werman, Michael},
  booktitle={2009 IEEE 12th International Conference on Computer Vision},
  pages={460--467},
  year={2009},
  month={September},
  organization={IEEE}
}