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author | glisse <glisse@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-12-12 05:43:06 +0000 |
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committer | glisse <glisse@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-12-12 05:43:06 +0000 |
commit | ad6a64ad5a4f4121410250021eda0904eb9c718c (patch) | |
tree | fdad2e783a79b388cde1826e3b344d8977d1183a /src/Witness_complex/doc/Witness_complex_doc.h | |
parent | f9a32a464156dd61b444f0e70c8342642363e8ea (diff) | |
parent | f0e5330a88f9e89a887769ab79f6db6dd4e1c35a (diff) |
Merge from trunk.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/qt5@1848 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: c8e1376894207c8c08896f750f71c115e07f6d95
Diffstat (limited to 'src/Witness_complex/doc/Witness_complex_doc.h')
-rw-r--r-- | src/Witness_complex/doc/Witness_complex_doc.h | 42 |
1 files changed, 42 insertions, 0 deletions
diff --git a/src/Witness_complex/doc/Witness_complex_doc.h b/src/Witness_complex/doc/Witness_complex_doc.h new file mode 100644 index 00000000..60dfd27b --- /dev/null +++ b/src/Witness_complex/doc/Witness_complex_doc.h @@ -0,0 +1,42 @@ +#ifndef WITNESS_COMPLEX_DOC_H_ +#define WITNESS_COMPLEX_DOC_H_ + +/** + \defgroup witness_complex Witness complex + + \author Siargey Kachanovich + + \image html "Witness_complex_representation.png" "Witness complex representation" + + \section Definitions + + Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$: + + \li \f$W\f$ set of **witnesses** and + \li \f$L \subseteq W\f$ set of **landmarks**. + + The simplices are based on landmarks + and a simplex belongs to the witness complex if and only if it is witnessed, that is: + + \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that + w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well. + + The data structure is described in \cite boissonnatmariasimplextreealgorithmica . + + \section Implementation + + The principal class of this module is Gudhi::Witness_complex. + + In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a witness and consists of landmarks sorted by distance to this witness. + This table can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module. + + *\image html "bench_Cy8.png" "Running time as function on number of landmarks" width=10cm + *\image html "bench_sphere.png" "Running time as function on number of witnesses for |L|=300" width=10cm + + + \copyright GNU General Public License v3. + + + */ + +#endif // WITNESS_COMPLEX_DOC_H_ |