From 4adbdcf16f311b0b5151311f77cfead5bf065bf4 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Tue, 31 Mar 2020 11:22:50 +0200 Subject: removed barycenters specific doc files as those are included in wasserstein distance now --- src/python/doc/barycenter_sum.inc | 24 --------------- src/python/doc/barycenter_user.rst | 60 -------------------------------------- 2 files changed, 84 deletions(-) delete mode 100644 src/python/doc/barycenter_sum.inc delete mode 100644 src/python/doc/barycenter_user.rst (limited to 'src/python/doc') diff --git a/src/python/doc/barycenter_sum.inc b/src/python/doc/barycenter_sum.inc deleted file mode 100644 index da2bdd84..00000000 --- a/src/python/doc/barycenter_sum.inc +++ /dev/null @@ -1,24 +0,0 @@ -.. table:: - :widths: 30 50 20 - - +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ - | .. figure:: | A Frechet mean (or barycenter) is a generalization of the arithmetic | :Author: Theo Lacombe | - | ./img/barycenter.png | mean in a non linear space such as the one of persistence diagrams. | | - | :figclass: align-center | Given a set of persistence diagrams :math:`\mu_1 \dots \mu_n`, it is | :Introduced in: GUDHI 3.1.0 | - | | defined as a minimizer of the variance functional, that is of | | - | Illustration of Frechet mean between persistence | :math:`\mu \mapsto \sum_{i=1}^n d_2(\mu,\mu_i)^2`. | :Copyright: MIT | - | diagrams. | where :math:`d_2` denotes the Wasserstein-2 distance between | | - | | persistence diagrams. | | - | | It is known to exist and is generically unique. However, an exact | | - | | computation is in general untractable. Current implementation | :Requires: Python Optimal Transport (POT) :math:`\geq` 0.5.1 | - | | available is based on [Turner et al, 2014], and uses an EM-scheme to | | - | | provide a local minimum of the variance functional (somewhat similar | | - | | to the Lloyd algorithm to estimate a solution to the k-means | | - | | problem). The local minimum returned depends on the initialization of| | - | | the barycenter. | | - | | The combinatorial structure of the algorithm limits its | | - | | scaling on large scale problems (thousands of diagrams and of points | | - | | per diagram). | | - +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ - | * :doc:`barycenter_user` | | - +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/barycenter_user.rst b/src/python/doc/barycenter_user.rst deleted file mode 100644 index 83e9bebb..00000000 --- a/src/python/doc/barycenter_user.rst +++ /dev/null @@ -1,60 +0,0 @@ -: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 ]] - - -- cgit v1.2.3