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-rw-r--r-- | src/Collapse/doc/intro_edge_collapse.h | 98 | ||||
-rw-r--r-- | src/Collapse/test/CMakeLists.txt | 9 | ||||
-rw-r--r-- | src/Collapse/test/collapse_unit_test.cpp | 94 |
3 files changed, 201 insertions, 0 deletions
diff --git a/src/Collapse/doc/intro_edge_collapse.h b/src/Collapse/doc/intro_edge_collapse.h new file mode 100644 index 00000000..b42b5e65 --- /dev/null +++ b/src/Collapse/doc/intro_edge_collapse.h @@ -0,0 +1,98 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Siddharth Pritam + * + * Copyright (C) 2019 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#ifndef DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ +#define DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ + +namespace Gudhi { + +namespace edge_collapse { + +/** \defgroup edge_collapse Edge collapse + * + * \author Siddharth Pritam + * + * @{ + * + * \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 + * \f$K\f$, \f$lk_K(e)\f$ is a simplicial cone, that is, there exists a vertex \f$v^{\prime} \notin e\f$ and a subcomplex + * \f$L\f$ in \f$K\f$, such that \f$lk_K(e) = v^{\prime}L\f$. We say that the vertex \f$v^{\prime}\f$ is {dominating} + * \f$e\f$ and \f$e\f$ is {dominated} by \f$v^{\prime}\f$. + * An <b> elementary egde collapse </b> is the removal of a dominated edge \f$e\f$ from \f$K\f$, + * which we denote with \f$K\f$ \f${\searrow\searrow}^1 \f$ \f$K\setminus e\f$. + * The symbol \f$\mathbf{K\setminus e}\f$ (deletion of \f$e\f$ from \f$K\f$) refers to the subcomplex of \f$K\f$ which + * has all simplices of \f$K\f$ except \f$e\f$ and the ones containing \f$e\f$. + * There is an <b>edge collapse</b> from a simplicial complex \f$K\f$ to its subcomplex \f$L\f$, + * if there exists a series of elementary edge collapses from \f$K\f$ to \f$L\f$, denoted as \f$K\f$ + * \f${\searrow\searrow}\f$ \f$L\f$. + * + * An edge collapse is a homotopy preserving operation, and it can be further expressed as sequence of the classical elementary simple collapse. + * A complex without any dominated edge is called a $1$- minimal complex and the core \f$K^1\f$ of simplicial comlex is a + * minimal complex such that \f$K\f$ \f${\searrow\searrow}\f$ \f$K^1\f$. + * Computation of a core (not unique) involves computation of dominated edges and the dominated edges can be easily + * characterized as follows: + * + * -- For general simplicial 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 maximal simplices of \f$K\f$ that contain $e$ also contain \f$v^{\prime}\f$ + * + * -- 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 (VR) 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. + * 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. + + * 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 increasing filtration value + * in the graph and check if the current edge \f$e_i\f$ is dominated in the current graph \f$G_i := \{e_1, .. e_i\} \f$ or not. + * If the edge \f$e_i\f$ is dominated we remove it from the filtration and move forward to the next edge \f$e_{i+1}\f$. + * If f$e_i\f$ is non-dominated then we keep it in the reduced filtration and then go backward in the current graph \f$G_i\f$ to look for new non-dominated edges + * that was dominated before but might become non-dominated at this point. + * If an edge \f$e_j, j < i \f$ during the backward search is found to be non-dominated, we include \f$\e_j\f$ in to the reduced filtration and we set its new filtration value to be $i$ that is the index of \f$e_i\f$. + * The precise mechanism for this reduction has been described in Section 5 \cite edgecollapsesocg2020. + * Here we implement this mechanism for a filtration of Rips complex, + * After perfoming the reduction the filtration reduces to a flag-filtration with the same persistence as the original filtration. + * + + * Comment: I think it would be good if you (Vincent) check the later part according to the examples you build. + * \subsection edge_collapse_from_points_example Example from a point cloud and a distance function + * + * This example builds the edge graph from the given points, threshold value, and distance function. + * Then it creates a `Flag_complex_edge_collapse` (exact version) with it. + * + * Then, it is asked to display the distance matrix after the collapse operation. + * + * \include Strong_collapse/strong_collapse_from_points.cpp + * + * \code $> ./strong_collapse_from_points + * \endcode + * + * the program output is: + * + * \include Strong_collapse/strong_collapse_from_points_for_doc.txt + * + * A `Gudhi::rips_complex::Rips_complex` can be built from the distance matrix if you want to compute persistence on + * top of it. + + * For more information about our approach of computing edge collapses and persitent homology via edge collapses, + * we refer the users to \cite edgecollapsesocg2020 . + * + */ +/** @} */ // end defgroup strong_collapse + +} // namespace edge_collapse + +} // namespace Gudhi + +#endif // DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ diff --git a/src/Collapse/test/CMakeLists.txt b/src/Collapse/test/CMakeLists.txt new file mode 100644 index 00000000..c7eafb46 --- /dev/null +++ b/src/Collapse/test/CMakeLists.txt @@ -0,0 +1,9 @@ +project(Collapse_tests) + +include(GUDHI_boost_test) + +add_executable ( Collapse_test_unit collapse_unit_test.cpp ) +if (TBB_FOUND) + target_link_libraries(Collapse_test_unit ${TBB_LIBRARIES}) +endif() +gudhi_add_boost_test(Collapse_test_unit) diff --git a/src/Collapse/test/collapse_unit_test.cpp b/src/Collapse/test/collapse_unit_test.cpp new file mode 100644 index 00000000..c2f08e57 --- /dev/null +++ b/src/Collapse/test/collapse_unit_test.cpp @@ -0,0 +1,94 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Vincent Rouvreau + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#include <iostream> +#include <fstream> +#include <string> +#include <algorithm> +#include <utility> // std::pair, std::make_pair +#include <cmath> // float comparison +#include <limits> +#include <functional> // greater +#include <tuple> // std::tie + +#define BOOST_TEST_DYN_LINK +#define BOOST_TEST_MODULE "collapse" +#include <boost/test/unit_test.hpp> +#include <boost/mpl/list.hpp> + +// ^ +// /!\ Nothing else from Simplex_tree shall be included to test includes are well defined. +#include "gudhi/FlagComplexSpMatrix.h" +#include "gudhi/Rips_edge_list.h" + +using namespace Gudhi; + +// Types definition +using Vector_of_points = std::vector<std::vector<double>>; + +using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>; +using Filtration_value = double; +using Rips_complex = Gudhi::rips_complex::Rips_complex<Filtration_value>; +using Rips_edge_list = Gudhi::rips_edge_list::Rips_edge_list<Filtration_value>; +using Field_Zp = Gudhi::persistent_cohomology::Field_Zp; +using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>; +using Distance_matrix = std::vector<std::vector<Filtration_value>>; + + +BOOST_AUTO_TEST_CASE(collapse) { + typedef size_t Vertex_handle; + typedef std::vector<std::tuple<Filtration_value, Vertex_handle, Vertex_handle>> Filtered_sorted_edge_list; + + std::size_t number_of_points; + std::string off_file_points; + std::string filediag; + int dim_max; + int p; + double min_persistence; + + Map map_empty; + + Distance_matrix sparse_distances; + + + Vector_of_points point_vector {{0., 0.},{0., 1.},{1., 0.},{1., 1.}}; + + int dimension = point_vector[0].dimension(); + number_of_points = point_vector.size(); + std::cout << "Successfully read " << number_of_points << " point_vector.\n"; + std::cout << "Ambient dimension is " << dimension << ".\n"; + + std::cout << "Point Set Generated." << std::endl; + + double threshold = 1.; + Filtered_sorted_edge_list edge_t; + std::cout << "Computing the one-skeleton for threshold: " << threshold << std::endl; + + Rips_edge_list Rips_edge_list_from_file(point_vector, threshold, Gudhi::Euclidean_distance()); + Rips_edge_list_from_file.create_edges(edge_t); + + std::cout << "Sorted edge list computed" << std::endl; + std::cout << "Total number of edges before collapse are: " << edge_t.size() << std::endl; + + if (edge_t.size() <= 0) { + std::cerr << "Total number of egdes are zero." << std::endl; + exit(-1); + } + + // Now we will perform filtered edge collapse to sparsify the edge list edge_t. + std::cout << "Filtered edge collapse begins" << std::endl; + FlagComplexSpMatrix mat_filt_edge_coll(number_of_points, edge_t); + std::cout << "Matrix instansiated" << std::endl; + Filtered_sorted_edge_list collapse_edges; + collapse_edges = mat_filt_edge_coll.filtered_edge_collapse(); + +} + + |