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author | Gard Spreemann <gspreemann@gmail.com> | 2017-02-07 17:33:01 +0100 |
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committer | Gard Spreemann <gspreemann@gmail.com> | 2017-02-07 17:33:01 +0100 |
commit | 55c7181126aa7defce38c9b82872d14223d4c1dd (patch) | |
tree | 7c683f014709459f066fd87a21da7f74cfc31a53 /doc/Witness_complex |
Initial import of upstream's 1.3.1.upstream/1.3.1
Diffstat (limited to 'doc/Witness_complex')
-rw-r--r-- | doc/Witness_complex/Witness_complex_doc.h | 42 | ||||
-rw-r--r-- | doc/Witness_complex/Witness_complex_representation.png | bin | 0 -> 48899 bytes | |||
-rw-r--r-- | doc/Witness_complex/bench_Cy8.png | bin | 0 -> 15254 bytes | |||
-rw-r--r-- | doc/Witness_complex/bench_sphere.png | bin | 0 -> 16614 bytes |
4 files changed, 42 insertions, 0 deletions
diff --git a/doc/Witness_complex/Witness_complex_doc.h b/doc/Witness_complex/Witness_complex_doc.h new file mode 100644 index 00000000..60dfd27b --- /dev/null +++ b/doc/Witness_complex/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_ diff --git a/doc/Witness_complex/Witness_complex_representation.png b/doc/Witness_complex/Witness_complex_representation.png Binary files differnew file mode 100644 index 00000000..1d31a490 --- /dev/null +++ b/doc/Witness_complex/Witness_complex_representation.png diff --git a/doc/Witness_complex/bench_Cy8.png b/doc/Witness_complex/bench_Cy8.png Binary files differnew file mode 100644 index 00000000..d9045294 --- /dev/null +++ b/doc/Witness_complex/bench_Cy8.png diff --git a/doc/Witness_complex/bench_sphere.png b/doc/Witness_complex/bench_sphere.png Binary files differnew file mode 100644 index 00000000..ba6bb381 --- /dev/null +++ b/doc/Witness_complex/bench_sphere.png |