Aardvark.jl
This library calculates the Earth Mover Distance between two one-dimensional vectors with a custom cost matrix. It uses the network simplex algorithm to compute the cost of the optimal transport problem and is the fastest implementation of EMD, I have found so far. However, in certain situations the network simplex algorithm fails to converge to a solution where one exists. I originally based this project on the Cython wrapper from POT. However, it seems in the meantime the people writing the original code have setup up their own repository as well.
In any case the original code is based on this paper:
@article{BPPH11, author = {Bonneel, Nicolas and van de Panne, Michiel and Paris, Sylvain and Heidrich, Wolfgang},
title = {{Displacement Interpolation Using Lagrangian Mass Transport}},
journal = {ACM Transactions on Graphics (SIGGRAPH ASIA 2011)},
volume = {30},
number = {6},
year = {2011},
}
Please cite the paper if you use this package for a publication.
Project Status
This project is built agains julia 1.5 and in an early alpha version.
Build
Until I figure out how to build the C++ dependencies with BinaryBuilder.jl in a way that lets me use this library on NixoOS as well, you need to compile the C++ code yourself. That means a somehwat recent cmake needs to be in your environment when building this package. You also need openMp when compiling. On the plus side, this enables automatic multi-threading.
Usage
using Aardvark
using Distances
You can just call emd with two vectors and the cost matrix:
a = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
b = reverse(a)
M = pairwise(Euclidean(), transpose(a), dims=2)
emd(a, b, M)
Alternatively you can also define, a Metric:
D = EMD(M)
D(a, b)
TODO
- Update source [X]
- Find out how to ship compiled version that works on Nixos [ ]
- Do a benchmark [ ]
- Support more dimensions [?]
- Example of when the network simplex algorithm fails [ ]
- Write tests [ ]