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:orphan:
.. To get rid of WARNING: document isn't included in any toctree
Barycenter user manual
================================
Definition
----------
.. include:: barycenter_sum.inc
This implementation is based on ideas from "Frechet means for distribution of
persistence diagrams", Turner et al. 2014.
Function
--------
.. autofunction:: gudhi.barycenter.lagrangian_barycenter
Basic example
-------------
This example computes the Frechet mean (aka Wasserstein barycenter) between
four persistence diagrams.
It is initialized on the 4th diagram.
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
as initial estimate.
Note that persistence diagrams must be submitted as
(n x 2) numpy arrays and must not contain inf values.
.. testcode::
import gudhi.barycenter
import numpy as np
dg1 = np.array([[0.2, 0.5]])
dg2 = np.array([[0.2, 0.7]])
dg3 = np.array([[0.3, 0.6], [0.7, 0.8], [0.2, 0.3]])
dg4 = np.array([])
pdiagset = [dg1, dg2, dg3, dg4]
bary = gudhi.barycenter.lagrangian_barycenter(pdiagset=pdiagset,init=3)
message = "Wasserstein barycenter estimated:"
print(message)
print(bary)
The output is:
.. testoutput::
Wasserstein barycenter estimated:
[[0.27916667 0.55416667]
[0.7375 0.7625 ]
[0.2375 0.2625 ]]
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