Detailed Description

Algorithms for finding the min-normalized-cut of a weighted undirected graph.

Two static methods are provided, one for bisection and the other for iterative N-parts partition. It is based on the Shi-Malik method, proposed for example in:

J. Shi and J. Malik, "Normalized Cuts and Image Segmentation,"IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, no.8, pp. 888-905, Aug. 2000.

Definition at line 47 of file CGraphPartitioner.h.

#include <mrpt/math/CGraphPartitioner.h>

Inheritance diagram for mrpt::math::CGraphPartitioner:

[legend]

List of all members.

Static Public Member Functions
static void	RecursiveSpectralPartition (CMatrix &in_A, std::vector< vector_uint > &out_parts, float threshold_Ncut=1.0f, bool forceSimetry=true, bool useSpectralBisection=true, bool recursive=true, unsigned minSizeClusters=1)
	Performs the spectral recursive partition into K-parts for a given graph.
static void	SpectralBisection (CMatrix &in_A, vector_uint &out_part1, vector_uint &out_part2, float &out_cut_value, bool forceSimetry=true)
	Performs the spectral bisection of a graph.
static void	exactBisection (CMatrix &in_A, vector_uint &out_part1, vector_uint &out_part2, float &out_cut_value, bool forceSimetry=true)
	Performs an EXACT minimum n-Cut graph bisection, (Use CGraphPartitioner::SpectralBisection for a faster algorithm)
static float	nCut (const CMatrix &in_A, const vector_uint &in_part1, const vector_uint &in_part2)
	Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection:
Static Public Attributes
static bool	DEBUG_SAVE_EIGENVECTOR_FILES
	If set to true (default=false), each eigenvector computed (and the laplacian of the adj.
static bool	VERBOSE
	If set to true (default=false), debug info will be displayed to cout.
Static Private Attributes
static int	debug_file_no
	Used internally when DEBUG_SAVE_EIGENVECTOR_FILES=true.

Member Function Documentation

static void mrpt::math::CGraphPartitioner::exactBisection	(	CMatrix &	in_A,
		vector_uint &	out_part1,
		vector_uint &	out_part2,
		float &	out_cut_value,
		bool	forceSimetry = `true`
	)		`[static]`

Performs an EXACT minimum n-Cut graph bisection, (Use CGraphPartitioner::SpectralBisection for a faster algorithm)

Parameters:

in_A	[IN] The weights matrix for the graph. It must be a square matrix, where element W_ij is the "likelihood" between nodes "i" and "j", and typically W_ii = 1.
out_part1	[OUT] The indexs of the nodes that fall into the first group.
out_part2	[OUT] The indexs of the nodes that fall into the second group.
out_cut_value	[OUT] The N-cut value for the proposed cut, in the range [0-2].
forceSimetry	[IN] If set to true (default) the elements W_ij and W_ji are replaced by 0.5·(W_ij+W_ji). Set to false if matrix is known to be simetric.

See also:: CMatrix, RecursiveSpectralPartition

Exceptions:

Throws a std::logic_error if an invalid matrix is passed.

static float mrpt::math::CGraphPartitioner::nCut	(	const CMatrix &	in_A,
		const vector_uint &	in_part1,
		const vector_uint &	in_part2
	)		`[static]`

Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection:

static void mrpt::math::CGraphPartitioner::RecursiveSpectralPartition	(	CMatrix &	in_A,
		std::vector< vector_uint > &	out_parts,
		float	threshold_Ncut = `1.0f`,
		bool	forceSimetry = `true`,
		bool	useSpectralBisection = `true`,
		bool	recursive = `true`,
		unsigned	minSizeClusters = `1`
	)		`[static]`

Performs the spectral recursive partition into K-parts for a given graph.

The default threshold for the N-cut is 1, which correspond to a cut equal of the geometric mean of self-associations of each pair of groups.

Parameters:

in_A	[IN] The weights matrix for the graph. It must be a square matrix, where element W_ij is the "likelihood" between nodes "i" and "j", and typically W_ii = 1.
out_parts	[OUT] An array of partitions, where each partition is represented as a vector of indexs for nodes.
threshold_Ncut	[IN] If it is desired to use other than the default threshold, it can be passed here.
forceSimetry	[IN] If set to true (default) the elements W_ij and W_ji are replaced by 0.5·(W_ij+W_ji). Set to false if matrix is known to be simetric.
useSpectralBisection	[IN] If set to true (default) a quick spectral bisection will be used. If set to false, a brute force, exact finding of the min-cut is performed.
recursive	[IN] Default=true, recursive algorithm for finding N partitions. Set to false to force 1 bisection as maximum.
minSizeClusters	[IN] Default=1, Minimum size of partitions to be accepted.

See also:: CMatrix, SpectralBisection

Exceptions:

Throws a std::logic_error if an invalid matrix is passed.

static void mrpt::math::CGraphPartitioner::SpectralBisection	(	CMatrix &	in_A,
		vector_uint &	out_part1,
		vector_uint &	out_part2,
		float &	out_cut_value,
		bool	forceSimetry = `true`
	)		`[static]`

Performs the spectral bisection of a graph.

This method always perform the bisection, and a measure of the goodness for this cut is returned.

Parameters:

in_A	[IN] The weights matrix for the graph. It must be a square matrix, where element W_ij is the "likelihood" between nodes "i" and "j", and typically W_ii = 1.
out_part1	[OUT] The indexs of the nodes that fall into the first group.
out_part2	[OUT] The indexs of the nodes that fall into the second group.
out_cut_value	[OUT] The N-cut value for the proposed cut, in the range [0-2].
forceSimetry	[IN] If set to true (default) the elements W_ij and W_ji are replaced by 0.5·(W_ij+W_ji). Set to false if matrix is known to be simetric.