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| author | Marc Glisse <marc.glisse@inria.fr> | 2020-05-12 23:00:30 +0200 |
|---|---|---|
| committer | Marc Glisse <marc.glisse@inria.fr> | 2020-05-12 23:00:30 +0200 |
| commit | 5631b0d1d9f7cc7e033e40fb9b94c8fe473f6082 (patch) | |
| tree | 5e52bb5b52b41a1b27053ad51bd72f8274d4c27a /src/python/doc/wasserstein_distance_user.rst | |
| parent | c5fca5477cc6fff77acedf7b5324eb5f8b417ed3 (diff) | |
| parent | 1efd71c502bacce375e1950e10a8112208acd0cf (diff) | |
Merge remote-tracking branch 'origin/master' into dtmdensity
Diffstat (limited to 'src/python/doc/wasserstein_distance_user.rst')
| -rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 15 |
1 files changed, 13 insertions, 2 deletions
diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index c443bab5..96ec7872 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -17,12 +17,21 @@ are measured in norm p, for :math:`1 \leq p \leq \infty`. Distance Functions ------------------ -This first implementation uses the Python Optimal Transport library and is based -on ideas from "Large Scale Computation of Means and Cluster for Persistence + +Optimal Transport +***************** + +:Requires: `Python Optimal Transport <installation.html#python-optimal-transport>`_ (POT) :math:`\geq` 0.5.1 + +This first implementation uses the `Python Optimal Transport <installation.html#python-optimal-transport>`_ +library and is based on ideas from "Large Scale Computation of Means and Cluster for Persistence Diagrams via Optimal Transport" :cite:`10.5555/3327546.3327645`. .. autofunction:: gudhi.wasserstein.wasserstein_distance +Hera +**** + This other implementation comes from `Hera <https://bitbucket.org/grey_narn/hera/src/master/>`_ (BSD-3-Clause) which is based on "Geometry Helps to Compare Persistence Diagrams" @@ -94,6 +103,8 @@ The output is: Barycenters ----------- +:Requires: `Python Optimal Transport <installation.html#python-optimal-transport>`_ (POT) :math:`\geq` 0.5.1 + A Frechet mean (or barycenter) is a generalization of the arithmetic mean in a non linear space such as the one of persistence diagrams. Given a set of persistence diagrams :math:`\mu_1 \dots \mu_n`, it is |