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Diffstat (limited to 'src/python/doc/rips_complex_user.rst')
| -rw-r--r-- | src/python/doc/rips_complex_user.rst | 4 |
1 files changed, 3 insertions, 1 deletions
diff --git a/src/python/doc/rips_complex_user.rst b/src/python/doc/rips_complex_user.rst index 1d340dbe..3f6b960d 100644 --- a/src/python/doc/rips_complex_user.rst +++ b/src/python/doc/rips_complex_user.rst @@ -19,7 +19,9 @@ The `Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>` generalizes proximity (:math:`\varepsilon`-ball) graphs to higher dimensions. The vertices correspond to the input points, and a simplex is present if and only if its diameter is smaller than some parameter α. Considering all parameters α defines a filtered simplicial complex, where the filtration value of a simplex is its diameter. -The filtration can be restricted to values α smaller than some threshold, to reduce its size. +The filtration can be restricted to values α smaller than some threshold, to reduce its size. Beware that some +people define the Rips complex using a bound of 2α instead of α, particularly when comparing it to an ambient +Čech complex. They end up with the same combinatorial object, but filtration values which are half of ours. The input discrete metric space can be provided as a point cloud plus a distance function, or as a distance matrix. |