diff options
| -rw-r--r-- | src/python/doc/wasserstein_distance_sum.inc | 6 | ||||
| -rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 10 |
2 files changed, 8 insertions, 8 deletions
diff --git a/src/python/doc/wasserstein_distance_sum.inc b/src/python/doc/wasserstein_distance_sum.inc index f10472bc..f9308e5e 100644 --- a/src/python/doc/wasserstein_distance_sum.inc +++ b/src/python/doc/wasserstein_distance_sum.inc @@ -4,10 +4,10 @@ +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ | .. figure:: | The q-Wasserstein distance measures the similarity between two | :Author: Theo Lacombe | | ../../doc/Bottleneck_distance/perturb_pd.png | persistence diagrams using the sum of all edges lengths (instead of | | - | :figclass: align-center | the maximum). It allows to define sophisticated objects such as | :Introduced in: GUDHI 3.1.0 | + | :figclass: align-center | the maximum). It allows to define sophisticated objects such as | :Since: GUDHI 3.1.0 | | | barycenters of a family of persistence diagrams. | | - | Wasserstein distance is the q-th root of the sum of the | | :Copyright: MIT | - | edge lengths to the power q. | | | + | | | :License: MIT | + | | | | | | | :Requires: Python Optimal Transport (POT) :math:`\geq` 0.5.1 | +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ | * :doc:`wasserstein_distance_user` | | diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index c6d49db1..c5c250b5 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -9,7 +9,7 @@ Definition .. include:: wasserstein_distance_sum.inc -The q-Wasserstein distance is defined as the minimal value +The q-Wasserstein distance is defined as the minimal value achieved by a perfect matching between the points of the two diagrams (+ all diagonal points), where the value of a matching is defined as the q-th root of the sum of all edge lengths to the power q. Edge lengths @@ -32,7 +32,7 @@ Morozov, and Arnur Nigmetov. .. 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. @@ -123,10 +123,10 @@ per diagram). diagrams. -.. autofunction:: gudhi.barycenter.lagrangian_barycenter +.. autofunction:: gudhi.wasserstein.barycenter.lagrangian_barycenter Basic example -------------- +************* This example estimates the Frechet mean (aka Wasserstein barycenter) between four persistence diagrams. @@ -135,7 +135,7 @@ As the algorithm is not convex, its output depends on the initialization and is only a local minimum of the objective function. Initialization can be either given as an integer (in which case the i-th diagram of the list is used as initial estimate) or as a diagram. -If None, it will randomly select one of the diagram of the list +If None, it will randomly select one of the diagrams of the list as initial estimate. Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values. |