Detailed Description
template<class GRAPH_MATRIX, typename num_t = typename GRAPH_MATRIX::Scalar>
class mrpt::graphs::CGraphPartitioner< GRAPH_MATRIX, num_t >
Algorithms for finding the min-normalized-cut of a weighted undirected graph.
Two methods are provided, one for bisection and the other for iterative N-parts partition. It 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 (e.g. mrpt::math::CMatrix) num_t The type of matrix elements, thresholds, etc. (typ: float or double). Defaults to the type of matrix elements.
- Note
- Prior to MRPT 1.0.0 this class wasn't a template and provided static variables for debugging, which were removed since that version.
Definition at line 36 of file CGraphPartitioner.h.
#include <mrpt/graphs/CGraphPartitioner.h>
Static Public Member Functions | |
| static void | RecursiveSpectralPartition (GRAPH_MATRIX &in_A, std::vector< vector_uint > &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, vector_uint &out_part1, vector_uint &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, vector_uint &out_part1, vector_uint &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 vector_uint &in_part1, const vector_uint &in_part2) |
| Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection: More... | |
Member Function Documentation
◆ exactBisection()
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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.
- Exceptions
-
Throws a std::logic_error if an invalid matrix is passed.
Definition at line 271 of file CGraphPartitioner_impl.h.
References ASSERT_, and THROW_EXCEPTION.
◆ nCut()
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static |
Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection:
Definition at line 229 of file CGraphPartitioner_impl.h.
◆ RecursiveSpectralPartition()
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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
- mrpt::math::CMatrix, SpectralBisection
- Exceptions
-
Throws a std::logic_error if an invalid matrix is passed.
Definition at line 101 of file CGraphPartitioner_impl.h.
References mrpt::format(), MRPT_END, MRPT_START, and THROW_EXCEPTION.
Referenced by mrpt::pbmap::SemanticClustering::evalPartition().
◆ SpectralBisection()
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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.
- Exceptions
-
Throws a std::logic_error if an invalid matrix is passed.
Definition at line 24 of file CGraphPartitioner_impl.h.
References eigenValues(), eigenVectors(), mean(), and THROW_EXCEPTION.