BinaryTree.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Binary space-partitioning tree of data points.
 * 
 * 
 *
 * \author      T. Glasmachers
 * \date        2011
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================

#ifndef SHARK_ALGORITHMS_NEARESTNEIGHBORS_BINARYTREE_H
#define SHARK_ALGORITHMS_NEARESTNEIGHBORS_BINARYTREE_H


#include <shark/Core/Exception.h>
#include <shark/Core/utility/functional.h>
#include <shark/Core/utility/KeyValuePair.h>
#include <shark/Models/Kernels/AbstractKernelFunction.h>

#include <boost/range/algorithm_ext/iota.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
namespace shark {


/// \brief Stopping criteria for tree construction.
///
/// \par
/// Conditions for automatic tree construction.
/// The data structure allows to specify a maximum
/// bucket size (number of instances represented
/// by a leaf), and a maximum tree depth.
///
/// \par
/// Note: If a data instance appears more often in
/// a dataset than specified by the maximum bucket
/// size then this condition will be violated; this
/// is because a space partitioning tree has no
/// means of separating a single point.
///
class TreeConstruction
{
public:
    /// \brief Default constructor: only stop at trivial leaves
    TreeConstruction()
    : m_maxDepth(0xffffffff)
    , m_maxBucketSize(1)
    { }

    /// \brief Copy constructor.
    TreeConstruction(TreeConstruction const& other)
    : m_maxDepth(other.m_maxDepth)
    , m_maxBucketSize(other.m_maxBucketSize)
    { }

    /// \brief Constructor.
    ///
    /// \param  maxDepth       stop as soon as the given tree depth is reached (zero means unrestricted)
    /// \param  maxBucketSize  stop as soon as a node holds at most the bucket size of data points (zero means unrestricted)
    TreeConstruction(unsigned int maxDepth, unsigned int maxBucketSize)
    : m_maxDepth(maxDepth ? maxDepth : 0xffffffff)
    , m_maxBucketSize(maxBucketSize ? maxBucketSize : 1)
    { }


    /// return a TreeConstruction object with maxDepth reduced by one
    TreeConstruction nextDepthLevel() const
    { return TreeConstruction(m_maxDepth - 1, m_maxBucketSize); }


    /// return maximum depth of the tree
    unsigned int maxDepth() const
    { return m_maxDepth; }

    /// return maximum "size" of a leaf node
    unsigned int maxBucketSize() const
    { return m_maxBucketSize; }

protected:
    /// maximum depth of the tree
    unsigned int m_maxDepth;

    /// maximum "size" of a leaf node
    unsigned int m_maxBucketSize;
};


///
/// \brief Super class of binary space-partitioning trees.
///
/// \par
/// This class represents a generic node in a binary
/// space-partitioning tree. At each junction the
/// space cell represented by the parent node is
/// split into sub-cells by thresholding a real-valued
/// function. Different sub-classes implement different
/// such functions. The absolute value of the function
/// minus the threshold m_threshold must represent the
/// distance to the separating hyper-surface in the
/// underlying metric. This allows for linear separation,
/// but also for kernel-induced feature spaces and other
/// embeddings.
template <class InputT>
class BinaryTree
{
public:
    typedef InputT value_type;

    /// \brief Root node constructor: build the tree from data.
    ///
    /// Please refer the specific sub-classes such as KDTree
    /// for examples of how the binary tree is built.
    ///
    BinaryTree(std::size_t size)
    : mep_parent(NULL)
    , mp_left(NULL)
    , mp_right(NULL)
    , mp_indexList(NULL)
    , m_size(size)
    , m_nodes(0)
    , m_threshold(0.0)
    {
        SHARK_ASSERT(m_size > 0);

        // prepare list of index/pointer pairs to be shared among the whole tree
        mp_indexList = new std::size_t[m_size];
        std::iota(mp_indexList,mp_indexList+m_size,0);
    }

    /// Destroy the tree and its internal data structures
    virtual ~BinaryTree()
    {
        if (mp_left != NULL) delete mp_left;
        if (mp_right != NULL) delete mp_right;
        if (mep_parent == NULL) delete [] mp_indexList;
    }


    // binary tree structure

    /// parent node
    BinaryTree* parent()
    { return mep_parent; }
    /// parent node
    const BinaryTree* parent() const
    { return mep_parent; }

    /// Does this node have children?
    /// Opposite of isLeaf()
    bool hasChildren() const
    { return (mp_left != NULL); }

    /// Is this a leaf node?
    /// Opposite of hasChildren()
    bool isLeaf() const
    { return (mp_left == NULL); }

    /// "left" sub-node of the binary tree
    BinaryTree* left()
    { return mp_left; }
    /// "left" sub-node of the binary tree
    const BinaryTree* left() const
    { return mp_left; }

    /// "right" sub-node of the binary tree
    BinaryTree* right()
    { return mp_right; }
    /// "right" sub-node of the binary tree
    const BinaryTree* right() const
    { return mp_right; }

    /// number of points inside the space represented by this node
    std::size_t size() const
    { return m_size; }

    /// number of sub-nodes in this tree (including the node itself)
    std::size_t nodes() const
    { return m_nodes; }

    std::size_t index(std::size_t point)const{
        return mp_indexList[point];
    }


    // partition represented by this node

    /// \brief Function describing the separation of space.
    ///
    /// \par
    /// This function is shifted by subtracting the
    /// threshold from the virtual function "funct" (which
    /// acts as a "decision" function to split space into
    /// sub-cells).
    /// The result of this function describes "signed"
    /// distance to the separation boundary, and the two
    /// cells are thresholded at zero. We obtain the two
    /// cells:<br/>
    /// left ("negative") cell: {x | distance(x) < 0}<br/>
    /// right ("positive") cell {x | distance(x) >= 0}
    double distanceFromPlane(value_type const& point) const{
        return funct(point) - m_threshold;
    }

    /// \brief Separation threshold.
    double threshold() const{
        return m_threshold;
    }

    /// return true if the reference point belongs to the
    /// "left" sub-node, or to the "negative" sub-cell.
    bool isLeft(value_type const& point) const
    { return (funct(point) < m_threshold); }

    /// return true if the reference point belongs to the
    /// "right" sub-node, or to the "positive" sub-cell.
    bool isRight(value_type const& point) const
    { return (funct(point) >= m_threshold); }

    /// \brief If the tree uses a kernel metric, returns a pointer to the kernel object, else NULL.
    virtual AbstractKernelFunction<value_type> const* kernel()const{
        //default is no kernel metric
        return NULL;
    }


    /// \brief Compute lower bound on the squared distance to the space cell.
    ///
    /// \par
    /// For efficient use of the triangle inequality
    /// the space cell represented by each node needs
    /// to provide (a lower bound on) the distance of
    /// a query point to the space cell represented by
    /// this node. Search is fast if this bound is
    /// tight.
    virtual double squaredDistanceLowerBound(value_type const& point) const = 0;

protected:
    /// \brief Sub-node constructor
    ///
    /// \par
    /// Initialize a sub-node
    BinaryTree(BinaryTree* parent, std::size_t* list, std::size_t size)
    : mep_parent(parent)
    , mp_left(NULL)
    , mp_right(NULL)
    , mp_indexList(list)
    , m_size(size)
    , m_nodes(0)
    {}


    /// \brief Function describing the separation of space.
    ///
    /// \par
    /// This is the primary interface for customizing
    /// sub-classes.
    ///
    /// \par
    /// This function splits the space represented by the
    /// node by thresholding at m_threshold. The "negative"
    /// cell, represented in the "left" sub-node, represents
    /// the space {x | funct(x) < threshold}. The
    /// "positive" cell, represented by the "right"
    /// sub-node, represents {x | funct(x) >= threshold}.
    /// The function needs to be normalized such that
    /// |f(x) - f(y)| is the distance between
    /// {z | f(z) = f(x)} and {z | f(z) = f(y)}, w.r.t.
    /// the distance function also used by the virtual
    /// function squaredDistanceLowerBound. The exact
    /// distance function does not matter as long as
    /// the same distance function is used in both cases.
    virtual double funct(value_type const& point) const = 0;

    /// \brief Split the data in the point list and calculate the treshold accordingly
    ///
    /// The method computes the optimal threshold given the distance of every element of
    /// the set and partitions the point range accordingly
    /// @param values the value of every point returned by funct(point)
    /// @param points the points themselves
    /// @returns returns the position were the point list was split
    template<class Range1, class Range2>
    typename Range2::iterator splitList (Range1& values, Range2& points){
        std::vector<KeyValuePair<typename Range1::value_type, typename Range2::value_type> > range(values.size());
        for(std::size_t i = 0; i != range.size(); ++i){
            range[i].key = values[i]; 
            range[i].value = points[i]; 
        }
        

        auto pos = partitionEqually(range);
        for(std::size_t i = 0; i != range.size(); ++i){
            values[i] = range[i].key;
            points[i] = range[i].value;
        }
        
        if (pos == range.end()) {
            // partitioning failed, all values are equal :(
            m_threshold = values[0];
            return points.begin();
        }

        // We don't want the threshold to be the value of an element but always in between two of them.
        // This ensures that no point of the training set lies on the boundary. This leeds to more stable
        // results. So we use the mean of the found splitpoint and the nearest point on the other side
        // of the boundary.
        double maximum = std::max_element(range.begin(), pos)->key;
        m_threshold = 0.5*(maximum + pos->key);

        return points.begin() + (pos - range.begin());
    }

    /// parent node
    BinaryTree* mep_parent;

    /// "left" child node
    BinaryTree* mp_left;

    /// "right" child node
    BinaryTree* mp_right;

    /// list of indices to points in the dataset
    std::size_t* mp_indexList;

    /// number of points in this node
    std::size_t m_size;

    /// number of nodes in the sub-tree represented by this node
    std::size_t m_nodes;

    /// threshold for the separating function
    double m_threshold;

};


}
#endif