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===================================== ===================================== =====================================
:Author: Siargey Kachanovich :Introduced in: GUDHI PYTHON 1.4.0 :Copyright: GPL v3
===================================== ===================================== =====================================
+---------------------------------------------+----------------------------------------------------------------------+
| .. image:: | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on |
| img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`:Wit(W,L)` is a simplicial |
| | complex defined on two sets of points in :math:`\mathbb{R}^D`: |
| | |
| | * :math:`W` set of **witnesses** and |
| | * :math:`L \subseteq W` set of **landmarks**. |
| | |
| | The simplices are based on landmarks and a simplex belongs to the |
| | witness complex if and only if it is witnessed, that is: |
| | |
| | :math:`\sigma \subset L` is witnessed if there exists a point |
| | :math:`w \in W` such that w is closer to the vertices of |
| | :math:`\sigma` than other points in :math:`L` and all of its faces |
| | are witnessed as well. |
| | |
| | The data structure is described in |
| | :cite:`boissonnatmariasimplextreealgorithmica`. |
+---------------------------------------------+----------------------------------------------------------------------+
| :doc:`witness_complex_user` | :doc:`witness_complex_ref` |
+---------------------------------------------+----------------------------------------------------------------------+
|
