From 6525c78704489b0c8cb62b2e3f882ce6113c0f0d Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Tue, 16 Apr 2019 23:19:19 +0200 Subject: Add min and max filtration values for the sparse Rips --- src/cython/doc/rips_complex_user.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'src/cython/doc/rips_complex_user.rst') diff --git a/src/cython/doc/rips_complex_user.rst b/src/cython/doc/rips_complex_user.rst index e814b4c3..1d340dbe 100644 --- a/src/cython/doc/rips_complex_user.rst +++ b/src/cython/doc/rips_complex_user.rst @@ -50,8 +50,8 @@ by more than the length used to define "too close". A more general technique is to use a sparse approximation of the Rips introduced by Don Sheehy :cite:`sheehy13linear`. We are using the version described in :cite:`buchet16efficient` (except that we multiply all filtration -values by 2, to match the usual Rips complex), which proves a -:math:`\frac{1+\varepsilon}{1-\varepsilon}`-interleaving, although in practice the +values by 2, to match the usual Rips complex). :cite:`cavanna15geometric` proves +a :math:`\frac{1}{1-\varepsilon}`-interleaving, although in practice the error is usually smaller. A more intuitive presentation of the idea is available in :cite:`cavanna15geometric`, and in a video :cite:`cavanna15visualizing`. Passing an extra argument `sparse=0.3` at the -- cgit v1.2.3