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:widths: 30 40 30
+----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+
- | .. figure:: | Rips complex is a simplicial complex constructed from a one skeleton | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse |
- | ../../doc/Rips_complex/rips_complex_representation.png | graph. | |
+ | .. figure:: | The Vietoris-Rips complex is a simplicial complex built as the | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse |
+ | ../../doc/Rips_complex/rips_complex_representation.png | clique-complex of a proximity graph. | |
| :figclass: align-center | | :Since: GUDHI 2.0.0 |
- | | The filtration value of each edge is computed from a user-given | |
- | | distance function and is inserted until a user-given threshold | :License: MIT |
- | | value. | |
+ | | We also provide sparse approximations, to speed-up the computation | |
+ | | of persistent homology, and weighted versions, which are more robust | :License: MIT |
+ | | to outliers. | |
| | | |
- | | This complex can be built from a point cloud and a distance function, | |
- | | or from a distance matrix. | |
- | | | |
- | | Weighted Rips complex constructs a simplicial complex from a distance | |
- | | matrix and weights on vertices. | |
+----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+
| * :doc:`rips_complex_user` | * :doc:`rips_complex_ref` |
+----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------+