:orphan:
.. To get rid of WARNING: document isn't included in any toctree
Wasserstein distance user manual
================================
Definition
----------
.. include:: wasserstein_distance_sum.inc
Functions
---------
This implementation is based on ideas from "Large Scale Computation of Means
and Cluster for Persistence Diagrams via Optimal Transport".
.. autofunction:: gudhi.wasserstein.wasserstein_distance
This other implementation comes from `Hera
`_ (BSD-3-Clause) and is
based on `"Geometry Helps to Compare Persistence Diagrams."
`_ by Michael Kerber, Dmitriy
Morozov, and Arnur Nigmetov, at ALENEX 2016.
.. autofunction:: gudhi.hera.wasserstein_distance
Basic example
-------------
This example computes the 1-Wasserstein distance from 2 persistence diagrams with euclidean ground metric.
Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values.
.. testcode::
import gudhi.wasserstein
import numpy as np
diag1 = np.array([[2.7, 3.7],[9.6, 14.],[34.2, 34.974]])
diag2 = np.array([[2.8, 4.45],[9.5, 14.1]])
message = "Wasserstein distance value = " + '%.2f' % gudhi.wasserstein.wasserstein_distance(diag1, diag2, q=2., p=1.)
print(message)
The output is:
.. testoutput::
Wasserstein distance value = 1.45