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author | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2020-06-02 22:45:38 +0200 |
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committer | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2020-06-02 22:45:38 +0200 |
commit | 50f9bb7d06bbf98c128513399a8f951870b074be (patch) | |
tree | d5cefa4f7a88b5e04b895905013dc1165d9ea0ed | |
parent | 796ebfdc2e6b6e3cdac18760f905ddf8dfc7367e (diff) |
doc review: Move a sentence as a module summary
-rw-r--r-- | src/Collapse/doc/intro_edge_collapse.h | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/src/Collapse/doc/intro_edge_collapse.h b/src/Collapse/doc/intro_edge_collapse.h index 82fadfb0..15f2208c 100644 --- a/src/Collapse/doc/intro_edge_collapse.h +++ b/src/Collapse/doc/intro_edge_collapse.h @@ -21,6 +21,10 @@ namespace collapse { * * @{ * + * This module implements edge collapse of a filtered flag complex, in particular it reduces a filtration of + * Vietoris-Rips complex from its graph to another smaller flag filtration with same persistence. + * Where a filtration is a sequence of simplicial (here Rips) complexes connected with inclusions. + * * \section edge_collapse_definition Edge collapse definition * * An edge \f$e\f$ in a simplicial complex \f$K\f$ is called a <b>dominated edge</b> if the link of \f$e\f$ in @@ -48,15 +52,11 @@ namespace collapse { * -- For a flag complex: An edge \f$e \in K\f$ is dominated by another vertex \f$v^{\prime} \in K\f$, <i>if and only * if</i> all the vertices in \f$K\f$ that has an edge with both vertices of \f$e\f$ also has an edge with * \f$v^{\prime}\f$. - - * This module implements edge collapse of a filtered flag complex, in particular it reduces a filtration of - * Vietoris-Rips complex from its graph - * to another smaller flag filtration with same persistence. Where a filtration is a sequence of simplicial - * (here Rips) complexes connected with inclusions. The algorithm to compute the smaller induced filtration is - * described in Section 5 \cite edgecollapsesocg2020. + * + * The algorithm to compute the smaller induced filtration is described in Section 5 \cite edgecollapsesocg2020. * Edge collapse can be successfully employed to reduce any given filtration of flag complexes to a smaller induced - * filtration which preserves the persistent homology of the original filtration and is a flag complex as well. - + * filtration which preserves the persistent homology of the original filtration and is a flag complex as well. + * * The general idea is that we consider edges in the filtered graph and sort them according to their filtration value * giving them a total order. * Each edge gets a unique index denoted as \f$i\f$ in this order. To reduce the filtration, we move forward with |