mrpt::graphs::CGraphPartitioner< GRAPH_MATRIX, num_t > Class Template Reference

Detailed Description

template<class GRAPH_MATRIX, typename num_t = typename GRAPH_MATRIX::Scalar>
class mrpt::graphs::CGraphPartitioner< GRAPH_MATRIX, num_t >

Finds the min-normalized-cut of a weighted undirected graph.

Two methods are provided:

• SpectralBisection(): Bisection.
• RecursiveSpectralPartition(): Iterative N-parts partition.

This is an implementation of the Shi-Malik method proposed 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.

Template Parameters

GRAPH_MATRIX	The type of square matrices used to represent the connectivity in a graph. Supported types are: mrpt::math::CMatrixDouble, mrpt::math::CMatrixD, mrpt::math::CMatrixFloat, mrpt::math::CMatrixF
num_t	The type of matrix elements, thresholds, etc. (double or float). Defaults to the type of matrix elements.

Definition at line 39 of file CGraphPartitioner.h.

#include <mrpt/graphs/CGraphPartitioner.h>

Static Public Member Functions
static void	RecursiveSpectralPartition (GRAPH_MATRIX &in_A, std::vector< std::vector< uint32_t >> &out_parts, num_t threshold_Ncut=1, bool forceSimetry=true, bool useSpectralBisection=true, bool recursive=true, unsigned minSizeClusters=1, const bool verbose=false)
	Performs the spectral recursive partition into K-parts for a given graph. More...
static void	SpectralBisection (GRAPH_MATRIX &in_A, std::vector< uint32_t > &out_part1, std::vector< uint32_t > &out_part2, num_t &out_cut_value, bool forceSimetry=true)
	Performs the spectral bisection of a graph. More...
static void	exactBisection (GRAPH_MATRIX &in_A, std::vector< uint32_t > &out_part1, std::vector< uint32_t > &out_part2, num_t &out_cut_value, bool forceSimetry=true)
	Performs an EXACT minimum n-Cut graph bisection, (Use CGraphPartitioner::SpectralBisection for a faster algorithm) More...
static num_t	nCut (const GRAPH_MATRIX &in_A, const std::vector< uint32_t > &in_part1, const std::vector< uint32_t > &in_part2)
	Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection: More...

Member Function Documentation

exactBisection()

template<class GRAPH_MATRIX , typename num_t >

void CGraphPartitioner::exactBisection ( GRAPH_MATRIX &  in_A, std::vector< uint32_t > &  out_part1, std::vector< uint32_t > &  out_part2, num_t &  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 Wij is the "likelihood" between nodes "i" and "j", and typically Wii = 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 Wij and Wji are replaced by 0.5*(Wij+Wji). Set to false if matrix is known to be simetric.

See also

mrpt::math::CMatrixF, RecursiveSpectralPartition

Exceptions

Throws

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

Definition at line 267 of file CGraphPartitioner.cpp.

References ASSERT_, mrpt::containers::end(), and THROW_EXCEPTION.

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nCut()

template<class GRAPH_MATRIX , typename num_t >

num_t CGraphPartitioner::nCut ( const GRAPH_MATRIX &  in_A, const std::vector< uint32_t > &  in_part1, const std::vector< uint32_t > &  in_part2  )

static

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

Definition at line 230 of file CGraphPartitioner.cpp.

RecursiveSpectralPartition()

template<class GRAPH_MATRIX , typename num_t >

void CGraphPartitioner::RecursiveSpectralPartition ( GRAPH_MATRIX &  in_A, std::vector< std::vector< uint32_t >> &  out_parts, num_t  threshold_Ncut = 1, bool  forceSimetry = true, bool  useSpectralBisection = true, bool  recursive = true, unsigned  minSizeClusters = 1, const bool  verbose = false  )

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 Wij is the "likelihood" between nodes "i" and "j", and typically Wii = 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 Wij and Wji are replaced by 0.5*(Wij+Wji). 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

SpectralBisection

Exceptions

Throws

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

Definition at line 103 of file CGraphPartitioner.cpp.

References mrpt::format(), MRPT_END, MRPT_START, THROW_EXCEPTION, and verbose.

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SpectralBisection()

template<class GRAPH_MATRIX , typename num_t >

void CGraphPartitioner::SpectralBisection ( GRAPH_MATRIX &  in_A, std::vector< uint32_t > &  out_part1, std::vector< uint32_t > &  out_part2, num_t &  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 Wij is the "likelihood" between nodes "i" and "j", and typically Wii = 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 Wij and Wji are replaced by 0.5*(Wij+Wji). Set to false if matrix is known to be simetric.

See also

mrpt::math::CMatrixF, RecursiveSpectralPartition

Exceptions

Throws

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

Definition at line 26 of file CGraphPartitioner.cpp.

References mrpt::math::laplacian(), mrpt::math::mean(), and THROW_EXCEPTION.

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