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Diffstat (limited to 'src/python/doc')
-rw-r--r-- | src/python/doc/wasserstein_distance_sum.inc | 14 | ||||
-rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 39 |
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diff --git a/src/python/doc/wasserstein_distance_sum.inc b/src/python/doc/wasserstein_distance_sum.inc new file mode 100644 index 00000000..0263f80f --- /dev/null +++ b/src/python/doc/wasserstein_distance_sum.inc @@ -0,0 +1,14 @@ +.. table:: + :widths: 30 50 20 + + +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ + | .. figure:: | The p-Wasserstein distance measures the similarity between two | :Author: Theo Lacombe | + | ../../doc/Bottleneck_distance/perturb_pd.png | persistence diagrams. It's the minimum value c that can be achieve by| | + | :figclass: align-center | a perfect matching between the points of the two diagrams (+ all the | :Introduced in: GUDHI 2.0.0 | + | | diagonal points), where the value of a matching is defined as the | | + | Wasserstein distance is the p-th root of the sum of the | p-th root of the sum of all edges lengths to the power p. Edges | :Copyright: MIT (`GPL v3 </licensing/>`_) | + | edges lengths to the power p. | lengths are measured in norm q, for $1 \leq q \leq \infty$. | | + | | | :Requires: `Python Optimal Transport (POT)` | + +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ + | * :doc:`wasserstein_distance_user` | | + +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst new file mode 100644 index 00000000..a51cfb71 --- /dev/null +++ b/src/python/doc/wasserstein_distance_user.rst @@ -0,0 +1,39 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +Wasserstein distance user manual +=============================== +Definition +---------- + +.. include:: wasserstein_distance_sum.inc + +This implementation is based on ideas from "Large Scale Computation of Means and Cluster for Persistence Diagrams via Optimal Transport". + +Function +-------- +.. autofunction:: gudhi.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 + + 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_distance(diag1, diag2, q=2., p=1.) + print(message) + +The output is: + +.. testoutput:: + + Wasserstein distance value = 1.45 |