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| author | pdlotko <pdlotko@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-12-09 19:35:19 +0000 |
|---|---|---|
| committer | pdlotko <pdlotko@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-12-09 19:35:19 +0000 |
| commit | 74ab2f3b7d7d616c78d4c116ab5e8c629a7fe9d6 (patch) | |
| tree | 66edf914df2d88d2548dccb620e0c70ca983947a /src/Gudhi_stat/doc | |
| parent | b7b23c26b855b83d03870cfd90b001fa2dedfd86 (diff) | |
Ansvers to Marc's comments, part deux.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/gudhi_stat@1842 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 361a254ad0837a344801c46049e09fb3b271bb0c
Diffstat (limited to 'src/Gudhi_stat/doc')
| -rw-r--r-- | src/Gudhi_stat/doc/documentation.pdf | bin | 158173 -> 158097 bytes | |||
| -rw-r--r-- | src/Gudhi_stat/doc/documentation.tex | 2 |
2 files changed, 1 insertions, 1 deletions
diff --git a/src/Gudhi_stat/doc/documentation.pdf b/src/Gudhi_stat/doc/documentation.pdf Binary files differindex 40bbea28..db8a7f1a 100644 --- a/src/Gudhi_stat/doc/documentation.pdf +++ b/src/Gudhi_stat/doc/documentation.pdf diff --git a/src/Gudhi_stat/doc/documentation.tex b/src/Gudhi_stat/doc/documentation.tex index a2430fc6..e89a8434 100644 --- a/src/Gudhi_stat/doc/documentation.tex +++ b/src/Gudhi_stat/doc/documentation.tex @@ -134,7 +134,7 @@ The detailed description of algorithms used to compute persistence landscapes ca \section{Persistence Landscapes on a grid} \label{sec:landscapes_on_grid} -This is an alternative, not--exact, representation of persistence landscapes defined in the Section~\ref{sec:persistence_landscapes}. Unlike in the Section~\ref{sec:persistence_landscapes} we build a representation of persistence landscape by sampling its values on a finite, equally distributed grid of points. Since, the persistence landscapes that originate from persistence diagrams have slope $1$ or $-1$, we have an estimate of a region between the grid points where the landscape cab be located. That allows to estimate an error make when performing various operations on landscape. Note that we do not have a similar estimation when a landscape is obtained as an average of collection of landscapes, since in this case the slopes of the lines can be arbitrary and we cannot determine the region where the average landscape is located. +This is an alternative, not--exact, representation of persistence landscapes defined in the Section~\ref{sec:persistence_landscapes}. Unlike in the Section~\ref{sec:persistence_landscapes} we build a representation of persistence landscape by sampling its values on a finite, equally distributed grid of points. Since, the persistence landscapes that originate from persistence diagrams have slope $1$ or $-1$, we have an estimate of a region between the grid points where the landscape cab be located. That allows to estimate an error make when performing various operations on landscape. Note that for average landscapes the slope is in range $[-1,1]$ and similar estimate can be used. Due to a lack of rigorous description of the algorithms to deal with this non--rigorous representaion of persistence landscapes in the literature, we are providing a short discussion of them in below. |