Cover complex data structure. More...

Public Member Functions
void	set_type (const std::string &t)
	Specifies whether the type of the output simplicial complex. More...

void	set_verbose (bool verb=false)
	Specifies whether the program should display information or not. More...

void	set_subsampling (double constant, double power)
	Sets the constants used to subsample the data set. These constants are explained in [18]. More...

void	set_mask (int nodemask)
	Sets the mask, which is a threshold integer such that nodes in the complex that contain a number of data points which is less than or equal to this threshold are not displayed. More...

void	set_point_cloud_from_range (const std::vector< std::vector< double > > &point_cloud)
	Reads and stores the input point cloud from vector stored in memory. More...

bool	read_point_cloud (const std::string &off_file_name)
	Reads and stores the input point cloud from .(n)OFF file. More...

void	set_graph_from_file (const std::string &graph_file_name)
	Creates a graph G from a file containing the edges. More...

void	set_graph_from_OFF ()
	Creates a graph G from the triangulation given by the input .OFF file. More...

template<typename Distance >
void	set_graph_from_rips (double threshold, Distance distance)
	Creates a graph G from a Rips complex. More...

void	set_distances_from_range (const std::vector< std::vector< double > > &distance_matrix)
	Reads and stores the distance matrices from vector stored in memory. More...

template<typename Distance >
double	set_graph_from_automatic_rips (Distance distance, int N=100)
	Creates a graph G from a Rips complex whose threshold value is automatically tuned with subsampling—see [18]. More...

void	set_function_from_file (const std::string &func_file_name)
	Creates the function f from a file containing the function values. More...

void	set_function_from_coordinate (int k)
	Creates the function f from the k-th coordinate of the point cloud P. More...

template<class InputRange >
void	set_function_from_range (InputRange const &function)
	Creates the function f from a vector stored in memory. More...

double	set_automatic_resolution ()
	Computes the optimal length of intervals (i.e. the smallest interval length avoiding discretization artifacts—see [18]) for a functional cover. More...

void	set_resolution_with_interval_length (double reso)
	Sets a length of intervals from a value stored in memory. More...

void	set_resolution_with_interval_number (int reso)
	Sets a number of intervals from a value stored in memory. More...

void	set_gain (double g=0.3)
	Sets a gain from a value stored in memory (default value 0.3). More...

void	set_cover_from_function ()
	Creates a cover C from the preimages of the function f. More...

void	set_cover_from_file (const std::string &cover_file_name)
	Creates the cover C from a file containing the cover elements of each point (the order has to be the same as in the input file!). More...

template<typename Distance >
void	set_cover_from_Voronoi (Distance distance, int m=100)
	Creates the cover C from the Voronoï cells of a subsampling of the point cloud. More...

const std::vector< int > &	subpopulation (int c)
	Returns the data subset corresponding to a specific node of the created complex. More...

void	set_color_from_file (const std::string &color_file_name)
	Computes the function used to color the nodes of the simplicial complex from a file containing the function values. More...

void	set_color_from_coordinate (int k=0)
	Computes the function used to color the nodes of the simplicial complex from the k-th coordinate. More...

void	set_color_from_range (std::vector< double > color)
	Computes the function used to color the nodes of the simplicial complex from a vector stored in memory. More...

void	plot_DOT ()
	Creates a .dot file called SC.dot for neato (part of the graphviz package) once the simplicial complex is computed to get a visualization of its 1-skeleton in a .pdf file.

void	write_info ()
	Creates a .txt file called SC.txt describing the 1-skeleton, which can then be plotted with e.g. KeplerMapper.

void	plot_OFF ()
	Creates a .off file called SC.off for 3D visualization, which contains the 2-skeleton of the GIC. This function assumes that the cover has been computed with Voronoi. If data points are in 1D or 2D, the remaining coordinates of the points embedded in 3D are set to 0.

Persistence_diagram	compute_PD ()
	Computes the extended persistence diagram of the complex. More...

void	compute_distribution (unsigned int N=100)
	Computes bootstrapped distances distribution. More...

double	compute_distance_from_confidence_level (double alpha)
	Computes the bottleneck distance threshold corresponding to a specific confidence level. More...

double	compute_confidence_level_from_distance (double d)
	Computes the confidence level of a specific bottleneck distance threshold. More...

double	compute_p_value ()
	Computes the p-value, i.e. the opposite of the confidence level of the largest bottleneck distance preserving the points in the persistence diagram of the output simplicial complex. More...

template<typename SimplicialComplex >
void	create_complex (SimplicialComplex &complex)
	Creates the simplicial complex. More...

void	find_simplices ()
	Computes the simplices of the simplicial complex.

Detailed Description

template<typename Point>
class Gudhi::cover_complex::Cover_complex< Point >

Cover complex data structure.

The data structure is a simplicial complex, representing a Graph Induced simplicial Complex (GIC) or a Nerve, and whose simplices are computed with a cover C of a point cloud P, which often comes from the preimages of intervals covering the image of a function f defined on P. These intervals are parameterized by their resolution (either their length or their number) and their gain (percentage of overlap). To compute a GIC, one also needs a graph G built on top of P, whose cliques with vertices belonging to different elements of C correspond to the simplices of the GIC.

Examples:: Nerve_GIC/CoordGIC.cpp, Nerve_GIC/FuncGIC.cpp, Nerve_GIC/Nerve.cpp, and Nerve_GIC/VoronoiGIC.cpp.

Member Function Documentation

◆ compute_confidence_level_from_distance()

template<typename Point>

double Gudhi::cover_complex::Cover_complex< Point >::compute_confidence_level_from_distance ( double d )

inline

Computes the confidence level of a specific bottleneck distance threshold.

Parameters

[in] d Bottleneck distance.

◆ compute_distance_from_confidence_level()

template<typename Point>

double Gudhi::cover_complex::Cover_complex< Point >::compute_distance_from_confidence_level ( double alpha )

inline

Computes the bottleneck distance threshold corresponding to a specific confidence level.

Parameters

[in] alpha Confidence level.

◆ compute_distribution()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::compute_distribution ( unsigned int N = 100 )

inline

Computes bootstrapped distances distribution.

Parameters

[in] N number of bootstrap iterations.

◆ compute_p_value()

template<typename Point>

double Gudhi::cover_complex::Cover_complex< Point >::compute_p_value ( )

inline

Computes the p-value, i.e. the opposite of the confidence level of the largest bottleneck distance preserving the points in the persistence diagram of the output simplicial complex.

◆ compute_PD()

template<typename Point>

Persistence_diagram Gudhi::cover_complex::Cover_complex< Point >::compute_PD ( )

inline

Computes the extended persistence diagram of the complex.

◆ create_complex()

template<typename Point>

template<typename SimplicialComplex >

void Gudhi::cover_complex::Cover_complex< Point >::create_complex ( SimplicialComplex & complex )

inline

Creates the simplicial complex.

Parameters

[in] complex SimplicialComplex to be created.

◆ read_point_cloud()

template<typename Point>

bool Gudhi::cover_complex::Cover_complex< Point >::read_point_cloud ( const std::string & off_file_name )

inline

Reads and stores the input point cloud from .(n)OFF file.

Parameters

[in] off_file_name name of the input .OFF or .nOFF file.

◆ set_automatic_resolution()

template<typename Point>

double Gudhi::cover_complex::Cover_complex< Point >::set_automatic_resolution ( )

inline

Computes the optimal length of intervals (i.e. the smallest interval length avoiding discretization artifacts—see [18]) for a functional cover.

Returns: reso interval length used to compute the cover.

◆ set_color_from_coordinate()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_color_from_coordinate ( int k = 0 )

inline

Computes the function used to color the nodes of the simplicial complex from the k-th coordinate.

Parameters

[in] k coordinate to use (start at 0).

◆ set_color_from_file()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_color_from_file ( const std::string & color_file_name )

inline

Computes the function used to color the nodes of the simplicial complex from a file containing the function values.

Parameters

[in] color_file_name name of the input color file.

◆ set_color_from_range()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_color_from_range ( std::vector< double > color )

inline

Computes the function used to color the nodes of the simplicial complex from a vector stored in memory.

Parameters

[in] color input vector of values.

◆ set_cover_from_file()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_cover_from_file ( const std::string & cover_file_name )

inline

Creates the cover C from a file containing the cover elements of each point (the order has to be the same as in the input file!).

Parameters

[in] cover_file_name name of the input cover file.

◆ set_cover_from_function()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_cover_from_function ( )

inline

Creates a cover C from the preimages of the function f.

◆ set_cover_from_Voronoi()

template<typename Point>

template<typename Distance >

void Gudhi::cover_complex::Cover_complex< Point >::set_cover_from_Voronoi	(	Distance	distance,
		int	m = `100`
	)

inline

Creates the cover C from the Voronoï cells of a subsampling of the point cloud.

Parameters

[in]	distance	distance between the points.
[in]	m	number of points in the subsample.

◆ set_distances_from_range()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_distances_from_range ( const std::vector< std::vector< double > > & distance_matrix )

inline

Reads and stores the distance matrices from vector stored in memory.

Parameters

[in] distance_matrix input vector representing the distance matrix.

◆ set_function_from_coordinate()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_function_from_coordinate ( int k )

inline

Creates the function f from the k-th coordinate of the point cloud P.

Parameters

[in] k coordinate to use (start at 0).

◆ set_function_from_file()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_function_from_file ( const std::string & func_file_name )

inline

Creates the function f from a file containing the function values.

Parameters

[in] func_file_name name of the input function file.

◆ set_function_from_range()

template<typename Point>

template<class InputRange >

void Gudhi::cover_complex::Cover_complex< Point >::set_function_from_range ( InputRange const & function )

inline

Creates the function f from a vector stored in memory.

Parameters

[in] function input vector of values.

◆ set_gain()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_gain ( double g = 0.3 )

inline

Sets a gain from a value stored in memory (default value 0.3).

Parameters

[in] g gain.

◆ set_graph_from_automatic_rips()

template<typename Point>

template<typename Distance >

double Gudhi::cover_complex::Cover_complex< Point >::set_graph_from_automatic_rips	(	Distance	distance,
		int	N = `100`
	)

inline

Creates a graph G from a Rips complex whose threshold value is automatically tuned with subsampling—see [18].

Parameters

[in]	distance	distance between data points.
[in]	N	number of subsampling iteration (the default reasonable value is 100, but there is no guarantee on how to choose it).

Returns: delta threshold used for computing the Rips complex.

◆ set_graph_from_file()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_graph_from_file ( const std::string & graph_file_name )

inline

Creates a graph G from a file containing the edges.

Parameters

[in] graph_file_name name of the input graph file. The graph file contains one edge per line, each edge being represented by the IDs of its two nodes.

◆ set_graph_from_OFF()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_graph_from_OFF ( )

inline

Creates a graph G from the triangulation given by the input .OFF file.

◆ set_graph_from_rips()

template<typename Point>

template<typename Distance >

void Gudhi::cover_complex::Cover_complex< Point >::set_graph_from_rips	(	double	threshold,
		Distance	distance
	)

inline

Creates a graph G from a Rips complex.

Parameters

[in]	threshold	threshold value for the Rips complex.
[in]	distance	distance used to compute the Rips complex.

◆ set_mask()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_mask ( int nodemask )

inline

Sets the mask, which is a threshold integer such that nodes in the complex that contain a number of data points which is less than or equal to this threshold are not displayed.

Parameters

[in] nodemask integer.

◆ set_point_cloud_from_range()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_point_cloud_from_range ( const std::vector< std::vector< double > > & point_cloud )

inline

Reads and stores the input point cloud from vector stored in memory.

Parameters

[in] point_cloud input vector representing the point cloud. Each row is a point and each coordinate is a vector.

◆ set_resolution_with_interval_length()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_resolution_with_interval_length ( double reso )

inline

Sets a length of intervals from a value stored in memory.

Parameters

[in] reso length of intervals.

◆ set_resolution_with_interval_number()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_resolution_with_interval_number ( int reso )

inline

Sets a number of intervals from a value stored in memory.

Parameters

[in] reso number of intervals.

◆ set_subsampling()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_subsampling	(	double	constant,
		double	power
	)

inline

Sets the constants used to subsample the data set. These constants are explained in [18].

Parameters

[in]	constant	double.
[in]	power	double.

◆ set_type()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_type ( const std::string & t )

inline

Specifies whether the type of the output simplicial complex.

Parameters

[in] t std::string (either "GIC" or "Nerve").

◆ set_verbose()

template<typename Point>

void Gudhi::cover_complex::Cover_complex< Point >::set_verbose ( bool verb = false )

inline

Specifies whether the program should display information or not.

Parameters

[in] verb boolean (true = display info, false = do not display info).

◆ subpopulation()

template<typename Point>

const std::vector<int>& Gudhi::cover_complex::Cover_complex< Point >::subpopulation ( int c )

inline

Returns the data subset corresponding to a specific node of the created complex.

Parameters

[in] c ID of the node.

Returns: cover_back(c) vector of IDs of data points.

The documentation for this class was generated from the following file:

include/gudhi/GIC.h

Public Member Functions

Detailed Description

template<typename Point> class Gudhi::cover_complex::Cover_complex< Point >

Member Function Documentation

◆ compute_confidence_level_from_distance()

◆ compute_distance_from_confidence_level()

◆ compute_distribution()

◆ compute_p_value()

◆ compute_PD()

◆ create_complex()

◆ read_point_cloud()

◆ set_automatic_resolution()

◆ set_color_from_coordinate()

◆ set_color_from_file()

◆ set_color_from_range()

◆ set_cover_from_file()

◆ set_cover_from_function()

◆ set_cover_from_Voronoi()

◆ set_distances_from_range()

◆ set_function_from_coordinate()

◆ set_function_from_file()

◆ set_function_from_range()

◆ set_gain()

◆ set_graph_from_automatic_rips()

◆ set_graph_from_file()

◆ set_graph_from_OFF()

◆ set_graph_from_rips()

◆ set_mask()

◆ set_point_cloud_from_range()

◆ set_resolution_with_interval_length()

◆ set_resolution_with_interval_number()

◆ set_subsampling()

◆ set_type()

◆ set_verbose()

◆ subpopulation()

template<typename Point>
class Gudhi::cover_complex::Cover_complex< Point >