CGraphPartitioner.h

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/* +---------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)               |
   |                          http://www.mrpt.org/                             |
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   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file        |
   | See: http://www.mrpt.org/Authors - All rights reserved.                   |
   | Released under BSD License. See details in http://www.mrpt.org/License    |
   +---------------------------------------------------------------------------+ */
#ifndef CGRAPHPARTITIONER_H
#define CGRAPHPARTITIONER_H

#include <mrpt/utils/utils_defs.h>
#include <mrpt/utils/COutputLogger.h>
#include <mrpt/math/CMatrix.h>
#include <mrpt/math/ops_matrices.h>

namespace mrpt
{
        /** Abstract graph and tree data structures, plus generic graph algorithms
          * \ingroup  mrpt_graphs_grp
          */
        namespace graphs
        {
                /** 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:<br><br>
                 *  <code>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.</code><br>
                 *
                 * \tparam GRAPH_MATRIX The type of square matrices used to represent the connectivity in a graph (e.g. mrpt::math::CMatrix)
                 * \tparam 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.
                 */
                template <class GRAPH_MATRIX, typename num_t = typename GRAPH_MATRIX::Scalar>
                class CGraphPartitioner : public mrpt::utils::COutputLogger
                {
                public:
                        /** 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.
                         *
                         * \param in_A                   [IN] The weights matrix for the graph. It must be a square matrix, where element W<sub>ij</sub> is the "likelihood" between nodes "i" and "j", and typically W<sub>ii</sub> = 1.
                         * \param out_parts              [OUT] An array of partitions, where each partition is represented as a vector of indexs for nodes.
                         * \param threshold_Ncut [IN] If it is desired to use other than the default threshold, it can be passed here.
                         * \param forceSimetry   [IN] If set to true (default) the elements W<sub>ij</sub> and W<sub>ji</sub> are replaced by 0.5*(W<sub>ij</sub>+W<sub>ji</sub>). Set to false if matrix is known to be simetric.
                         * \param 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.
                         * \param recursive [IN] Default=true, recursive algorithm for finding N partitions. Set to false to force 1 bisection as maximum.
                         * \param minSizeClusters [IN] Default=1, Minimum size of partitions to be accepted.
                         *
                         * \sa mrpt::math::CMatrix, SpectralBisection
                         *
                         * \exception Throws a std::logic_error if an invalid matrix is passed.
                         */
                        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 bisection of a graph. This method always perform
                         *   the bisection, and a measure of the goodness for this cut is returned.
                         *
                         * \param in_A                  [IN] The weights matrix for the graph. It must be a square matrix, where element W<sub>ij</sub> is the "likelihood" between nodes "i" and "j", and typically W<sub>ii</sub> = 1.
                         * \param out_part1             [OUT] The indexs of the nodes that fall into the first group.
                         * \param out_part2             [OUT] The indexs of the nodes that fall into the second group.
                         * \param out_cut_value [OUT] The N-cut value for the proposed cut, in the range [0-2].
                         * \param forceSimetry  [IN] If set to true (default) the elements W<sub>ij</sub> and W<sub>ji</sub> are replaced by 0.5*(W<sub>ij</sub>+W<sub>ji</sub>). Set to false if matrix is known to be simetric.
                         *
                         * \sa mrpt::math::CMatrix, RecursiveSpectralPartition
                         *
                         * \exception Throws a std::logic_error if an invalid matrix is passed.
                         */
                        static void SpectralBisection(
                                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)
                         *
                         * \param in_A                  [IN] The weights matrix for the graph. It must be a square matrix, where element W<sub>ij</sub> is the "likelihood" between nodes "i" and "j", and typically W<sub>ii</sub> = 1.
                         * \param out_part1             [OUT] The indexs of the nodes that fall into the first group.
                         * \param out_part2             [OUT] The indexs of the nodes that fall into the second group.
                         * \param out_cut_value [OUT] The N-cut value for the proposed cut, in the range [0-2].
                         * \param forceSimetry  [IN] If set to true (default) the elements W<sub>ij</sub> and W<sub>ji</sub> are replaced by 0.5*(W<sub>ij</sub>+W<sub>ji</sub>). Set to false if matrix is known to be simetric.
                         *
                         * \sa mrpt::math::CMatrix, RecursiveSpectralPartition
                         *
                         * \exception Throws a std::logic_error if an invalid matrix is passed.
                         */
                        static void  exactBisection(
                                GRAPH_MATRIX    &in_A,
                                vector_uint             &out_part1,
                                vector_uint             &out_part2,
                                num_t                   &out_cut_value,
                                bool                    forceSimetry = true );

                        /** Returns the normaliced cut of a graph, given its adjacency matrix A and a bisection:
                          */
                        static num_t nCut(
                                const GRAPH_MATRIX              &in_A,
                                const vector_uint               &in_part1,
                                const vector_uint               &in_part2 );

                }; // End of class def.

        } // End of namespace
} // End of namespace

// Template implementation:
#include "CGraphPartitioner_impl.h"

#endif