File: knn.hpp

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/*
 *
 * Copyright (C) 2001-2005 Ichiro Fujinaga, Michael Droettboom, and Karl MacMillan
 *               2012      Tobias Bolten
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program 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 General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 */

#ifndef kwm08142002_knn
#define kwm08142002_knn

#include "gamera_limits.hpp"
#include <vector>
#include <map>
#include <cmath>
#include <algorithm>
#include <exception>
#include <stdexcept>
#include <cassert>

namespace Gamera {
  namespace kNN {
    /*
      DISTANCE FUNCTIONS
    */

    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the city block method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC: iterator tyoe for the selection vector
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD>
    inline double city_block_distance(IterA known, const IterA end,
                                      IterB unknown, IterC selection,
                                      IterD weight) {
      double distance = 0;
      for (; known != end; ++known, ++unknown, ++selection, ++weight) {
        distance += (*selection) * ((*weight) * std::abs((*unknown) - (*known)));
      }
      return distance;
    }


    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the euclidean method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC: iterator type for the selection vector
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD>
    inline double euclidean_distance(IterA known, const IterA end,
                                     IterB unknown, IterC selection,
                                     IterD weight) {
      double distance = 0;
      for (; known != end; ++known, ++unknown, ++selection, ++weight) {
        distance += (*selection) * ((*weight) *
            std::sqrt(((*unknown) - (*known)) * ((*unknown) - (*known))));
      }
      return distance;
    }


    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the fast euclidean method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC: iterator type for the selection vector
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD>
    inline double fast_euclidean_distance(IterA known, const IterA end,
                                          IterB unknown, IterC selection,
                                          IterD weight) {
      double distance = 0;
      for (; known != end; ++known, ++unknown, ++selection, ++weight)
        distance += (*selection) * ((*weight) *
            (((*unknown) - (*known)) * ((*unknown) - (*known))));
      return distance;
    }

    /*
      DISTANCE FUNCTIONS with skip.
      
      These distance functions allow you to skip certain features in the
      feature vector. This allows you to evaluate a subset of feature
      vectors with leave-one-out, for example. This is done by passing
      in a list of indexes to be used for the distance calculation. For
      example, if you have a feature vector of length 4 and you want to
      skip the second feature, you would pass in an iterator pair for a
      container of [0, 2, 3].
    */

    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the city block method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC: iterator type for the selection vector
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD, class IterE>
    inline double city_block_distance_skip(IterA known, IterB unknown,
                                           IterC selection, IterD weight,
                                           IterE indexes, const IterE end) {
      double distance = 0;
      for (; indexes != end; ++indexes) {
        distance += selection[*indexes] * (weight[*indexes] *
            std::abs(unknown[*indexes] - known[*indexes]));
      }
      return distance;
    }


    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the euclidean method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC: iterator type fot the selection vector
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD, class IterE>
    inline double euclidean_distance_skip(IterA known, IterB unknown,
                                          IterC selection, IterD weight,
                                          IterE indexes, const IterE end) {
      double distance = 0;
      for (; indexes != end; ++indexes) {
        distance += selection[*indexes] * (weight[*indexes] *
            std::sqrt((unknown[*indexes] - known[*indexes]) * (unknown[*indexes] - known[*indexes])));
      }
      return distance;
    }


    /*
      Compute the weighted distance between a known feature
      and an unknown feature using the fast euclidean method.

      IterA: iterator type for the known feature vector
      IterB: iterator type for the unknown feature vector
      IterC:
      IterD: iterator type for the weighting vector
    */
    template<class IterA, class IterB, class IterC, class IterD, class IterE>
    inline double fast_euclidean_distance_skip(IterA known, IterB unknown,
                                               IterC selection, IterD weight,
                                               IterE indexes, const IterE end) {
      double distance = 0;
      for (; indexes != end; ++indexes) {
        distance += selection[*indexes] * (weight[*indexes] *
            ((unknown[*indexes] - known[*indexes]) * (unknown[*indexes] - known[*indexes])));
      }
      return distance;
    }

    /*
      NORMALIZE
      
      Normalize is used to compute normalization of the feature vectors in a database
      of known feature vectors and then to apply that normalization to feature
      vectors. It only works with doubles.

      Like the kNearestNeighbors class below, Normalize avoids knowing
      anything about the data structures used for storing the feature
      vectors. The add method is called for each feature vector,
      compute_normalization is called, and then feature vectors can
      be normalized by calling apply.
    */
    class Normalize {
    public:
      Normalize(size_t num_features) {
        m_num_features = num_features;
        m_num_feature_vectors = 0;
        m_mean_vector = new double[m_num_features];
        std::fill(m_mean_vector, m_mean_vector + m_num_features, 0.0);
        m_stdev_vector = new double[m_num_features];
        std::fill(m_stdev_vector, m_stdev_vector + m_num_features, 0.0);
        m_sum_vector = new double[m_num_features];
        std::fill(m_sum_vector, m_sum_vector + m_num_features, 0.0);
        m_sum2_vector = new double[m_num_features];
        std::fill(m_sum2_vector, m_sum2_vector + m_num_features, 0.0);
      }
      ~Normalize() {
        if (m_sum_vector != 0)
          delete[] m_sum_vector;
        if (m_sum2_vector != 0)
          delete[] m_sum2_vector;

        delete[] m_mean_vector;
        delete[] m_stdev_vector;
      }
      template<class T>
      void add(T begin, const T end) {
        assert(m_sum_vector != 0 && m_sum2_vector != 0);
        if (size_t(end - begin) != m_num_features)
          throw std::range_error("Normalize: number features did not match.");
        for (size_t i = 0; begin != end; ++begin, ++i) {
          m_sum_vector[i] += *begin;
          m_sum2_vector[i] += *begin * *begin;
        }
        ++m_num_feature_vectors;
      }
      void compute_normalization() {
        assert(m_sum_vector != 0 && m_sum2_vector != 0);
        double mean, var, stdev, sum, sum2;
        for (size_t i = 0; i < m_num_features; ++i) {
          sum = m_sum_vector[i];
          sum2 = m_sum2_vector[i];
          mean = sum / m_num_feature_vectors;
          var = (m_num_feature_vectors * sum2 - sum * sum)
            / (m_num_feature_vectors * (m_num_feature_vectors - 1));
          stdev = std::sqrt(var);
          if (stdev < 0.00001)
            stdev = 0.00001;
          m_mean_vector[i] = mean;
          m_stdev_vector[i] = stdev;
        }
        delete[] m_sum_vector;
        m_sum_vector = 0;
        delete[] m_sum2_vector;
        m_sum2_vector = 0;
      }
      // in-place
      template<class T>
      void apply(T begin, const T end) const {
        assert(size_t(end - begin) == m_num_features);
        double* mean = m_mean_vector;
        double* stdev = m_stdev_vector;
        for (; begin != end; ++begin, ++mean, ++stdev)
          *begin = (*begin - *mean)/ *stdev;
      }
      // out-of-place
      template<class T, class U>
      void apply(T in_begin, const T end, U out_begin) const {
        assert(size_t(end - in_begin) == m_num_features);
        double *mean = m_mean_vector;
        double *stdev = m_stdev_vector;
        for (; in_begin != end; ++in_begin, ++mean, ++stdev, ++out_begin)
          *out_begin = (*in_begin - *mean) / *stdev;
      }
      size_t num_features() const {
        return m_num_features;
      }
      double* get_mean_vector() const {
        return m_mean_vector;
      }
      double* get_stdev_vector() const {
        return m_stdev_vector;
      }
      template<class T>
      void set_mean_vector(T begin, const T end) {
        assert(size_t(end - begin) == m_num_features);
        double* cur = m_mean_vector;
        for (; begin != end; ++begin, ++cur)
          *cur = *begin;
        return;
      }
      template<class T>
      void set_stdev_vector(T begin, const T end) {
        assert(size_t(end - begin) == m_num_features);
        double* cur = m_stdev_vector;
        for (; begin != end; ++begin, ++cur)
          *cur = *begin;
        return;
      }
    private:
      size_t m_num_features;
      size_t m_num_feature_vectors;
      double* m_mean_vector;
      double* m_stdev_vector;
      double* m_sum_vector;
      double* m_sum2_vector;
    };

    /*
      K NEAREST NEIGHBORS

      This class holds a list of the k nearest neighbors and provides
      a method of querying for the id of the majority of neighbors. This
      class is meant to be used once - after calling add for each item in
      a database and majority the state of the class is undefined. If another
      search needs to be performed call reset (at which point add for each
      element will need to be called again).
    */
    template<class IdType, class CompLT, class CompEQ>
    class kNearestNeighbors {
    public:
      /*
        These nested classes are only used in kNearestNeighbors
      */

      /*
        NEIGHBOR
        
        This class holds the information needed for the Nearest Neighbor
        computation.
        
        IdType: the type for the id (possibilities includes longs
        and std::string)
      */
      class Neighbor {
      public:
        Neighbor(IdType id_, double distance_) {
          id = id_;
          distance = distance_;
        }
        bool operator<(const Neighbor& other) const {
          return distance < other.distance;
        }
        IdType id;
        double distance;
      };

      class IdStat {
      public:
        IdStat() {
          min_distance = std::numeric_limits<double>::max();
          count = 0;
        }
        IdStat(double distance, size_t c) {
          min_distance = distance;
          count = c;
        }
        double min_distance;
        double total_distance;
        size_t count;
      };

      // typedefs for convenience
      typedef IdType id_type;
      typedef Neighbor neighbor_type;
      typedef std::vector<neighbor_type> vec_type;

      // Constructor
      kNearestNeighbors(size_t k = 1) : m_k(k) {
        m_max_distance = 0;
        m_nun = NULL;
      }
      // Destructor
      ~kNearestNeighbors() {
        if (m_nun) delete m_nun;
      }
      // Reset the class to its initial state
      void reset() {
        m_nn.clear();
        m_max_distance = 0;
        if (m_nun) delete m_nun;
        m_nun = NULL;
      }
      /*
        Attempt to add a neighbor to the list of k closest
        neighbors. The list of neighbors is always kept sorted
        so that the largest distance is the last element.
      */
      void add(const id_type id, double distance) {
        // update nearest unlike neighbor
        if (!m_nn.empty() && !ceq(m_nn[0].id,id)) {
          if (!m_nun) {
            if (distance < m_nn[0].distance)
              m_nun = new neighbor_type(m_nn[0].id, m_nn[0].distance);
            else
              m_nun = new neighbor_type(id, distance);
          } else {
            if (distance < m_nn[0].distance) {
              m_nun->id = m_nn[0].id;
              m_nun->distance = m_nn[0].distance;
            }
            else if (distance < m_nun->distance) {
              m_nun->id = id;
              m_nun->distance = distance;
            }
          }
        }
        // update list of k nearest neighbors
        if (m_nn.size() < m_k) {
          m_nn.push_back(neighbor_type(id, distance));
          std::sort(m_nn.begin(), m_nn.end());
        } else if (distance < m_nn.back().distance) {
          m_nn.back().distance = distance;
          m_nn.back().id = id;
          std::sort(m_nn.begin(), m_nn.end());
        }
        if (distance > m_max_distance)
          m_max_distance = distance;
      }
      /*
        Find the id of the majority of the k nearest neighbors. This
        includes tie-breaking if necessary.
      */
      void majority() {
        answer.clear();
        
        if (m_nn.size() == 0)
          throw std::range_error("majority called without enough valid neighbors.");
        // short circuit for k == 1
        if (m_nn.size() == 1) {
          answer.resize(1);
          answer[0] = std::make_pair(m_nn[0].id, m_nn[0].distance);
          return;
        }
        /*
          Create a histogram of the ids in the nearest neighbors. A map
          is used because the id_type could be anything. Additionally, even
          if id_type was an integer there is no garuntee that they are small,
          ordered numbers (making a vector impractical).
        */
        typedef std::map<id_type, IdStat, CompLT> map_type;
        map_type id_map;
        typename map_type::iterator current;
        for (typename vec_type::iterator i = m_nn.begin();
             i != m_nn.end(); ++i) {
          current = id_map.find(i->id);
          if (current == id_map.end()) {
            id_map.insert(std::pair<id_type,
                          IdStat>(i->id, IdStat(i->distance, 1)));
          } else {
            current->second.count++;
            current->second.total_distance += i->distance;
            if (current->second.min_distance > i->distance)
              current->second.min_distance = i->distance;
          }
        }
        /*
          Now that we have the histogram we can take the majority if there
          is a clear winner, but if not, we need do some sort of tie breaking.
        */
        if (id_map.size() == 1) {
          answer.resize(1);
          answer[0] = std::make_pair(id_map.begin()->first, id_map.begin()->second.min_distance);
          return;
        } else {
          /*
            Find the id(s) with the maximum
          */
          std::vector<typename map_type::iterator> max;
          max.push_back(id_map.begin());
          for (typename map_type::iterator i = id_map.begin();
               i != id_map.end(); ++i) {
            if (i->second.count > max[0]->second.count) {
              max.clear();
              max.push_back(i);
            } else if (i->second.count == max[0]->second.count) {
              max.push_back(i);
            }
          }
          /*
            If the vector only has 1 element there are no ties and
            we are done.
          */
          if (max.size() == 1) {
            // put the winner in the result vector
            answer.push_back(std::make_pair(max[0]->first, max[0]->second.min_distance));
            // remove the winner from the id_map
            id_map.erase(max[0]);
          } else {
            /*
              Tie-break by average distance
            */
            typename map_type::iterator min_dist = max[0];
            for (size_t i = 1; i < max.size(); ++i) {
              if (max[i]->second.total_distance
                  < min_dist->second.total_distance)
                min_dist = max[i];
            }
            answer.push_back(std::make_pair(min_dist->first, min_dist->second.min_distance));
            id_map.erase(min_dist);
          }
          for (typename map_type::iterator i = id_map.begin();
               i != id_map.end(); ++i) {
            // Could not figure out why distance should be < 1 for additional
            // classes => let us instead return all classes among kNN (CD)
            //if (i->second.min_distance < 1)
            answer.push_back(std::make_pair(i->first, i->second.min_distance));
          }
          return;
        }
      }
      void calculate_confidences() {
        size_t i,j;
        static double epsilonmin = std::numeric_limits<double>::min();
        static double epsilon = std::numeric_limits<double>::epsilon();
        confidence.clear();
        if (answer.empty()) return;
        for (i = 0; i < confidence_types.size(); ++i) {
          if (CONFIDENCE_DEFAULT == confidence_types[i]) {
            confidence.push_back(get_default_confidence(answer[0].second));
          }
          // fraction of main class among k nearest neighbors
          else if (CONFIDENCE_KNNFRACTION == confidence_types[i]) {
            size_t m = 0;
            id_type mainid = answer[0].first;
            for (j = 0; j < m_nn.size(); ++j) {
              if (ceq(m_nn[j].id, mainid)) {
                m++;
              }
            }
            confidence.push_back(((double)m)/m_nn.size());
          }
          // inversely weighted average
          else if (CONFIDENCE_INVERSEWEIGHT == confidence_types[i]) {
            id_type mainid = answer[0].first;
            if (m_nn[0].distance < 256*epsilonmin) {
              // zero distance => compute fraction among zero distances
              size_t m = 1;
              size_t n = 1;
              for (j = 1; j < m_nn.size(); ++j) {
                if (m_nn[j].distance < 256*epsilonmin) {
                  n++;
                  if (ceq(m_nn[j].id, mainid))
                    m++;
                }
              }
              confidence.push_back(((double)m)/n);
            } else {
              double numerator = 0.0;
              double denominator = 0.0;
              double weight;
              for (j = 0; j < m_nn.size(); ++j) {
                weight = 1 / m_nn[j].distance;
                denominator += weight;
                if (ceq(m_nn[j].id, mainid))
                  numerator += weight;
              }
              confidence.push_back(numerator/denominator);
            }
          }
          // linearly weighted average
          else if (CONFIDENCE_LINEARWEIGHT == confidence_types[i]) {
            id_type mainid = answer[0].first;
            if (1.0 - m_nn[0].distance / m_nn.back().distance < 8*epsilon) {
              // distance to all neighbors equal => compute knn fraction
              size_t m = 0;
              for (j = 0; j < m_nn.size(); ++j) {
                if (ceq(m_nn[j].id, mainid))
                  m++;
              }
              confidence.push_back(((double)m)/m_nn.size());
            } else {
              double maxdist = m_nn.back().distance;
              double scale = maxdist - m_nn[0].distance;
              double numerator = 0.0;
              double denominator = 0.0;
              double weight;
              for (j = 0; j < m_nn.size(); ++j) {
                weight = (maxdist - m_nn[j].distance) / scale;
                denominator += weight;
                if (ceq(m_nn[j].id, mainid))
                  numerator += weight;
              }
              confidence.push_back(numerator/denominator);
            }
          }
          // nearest unlike neighbor confidence
          else if (CONFIDENCE_NUN == confidence_types[i]) {
            if (m_nun) {
              confidence.push_back(1 - answer[0].second / (m_nun->distance + epsilonmin));
            } else {
              confidence.push_back(1.0);
            }
          }
          // distance to nearest neighbor
          else if (CONFIDENCE_NNDISTANCE == confidence_types[i]) {
            confidence.push_back(answer[0].second);
          }
          // average distance to k nearest neighbors
          else if (CONFIDENCE_AVGDISTANCE == confidence_types[i]) {
            double distsum = 0.0;
            for (j = 0; j < m_nn.size(); ++j)
              distsum += m_nn[j].distance;
            confidence.push_back(distsum/m_nn.size());
          }
        }
        // for backward compatibility, we store MDB's confidence
        // with each answer class instead of the distance
        for (i = 0; i < answer.size(); ++i) {
          answer[i].second = get_default_confidence(answer[i].second);
        }
      }
    private:
      CompEQ ceq; // test whether two class id's are equal
      // simple measure that is defined for all classes and k values
      double get_default_confidence(double dist) {
        static double epsilonmin = std::numeric_limits<double>::min();
        return std::pow(1.0 - (dist / (m_max_distance + epsilonmin)), 10);
      }
    public:
      // list of classes and distances
      std::vector<std::pair<id_type, double> > answer;
      // confidence types and values for main class
      std::vector<int> confidence_types;
      std::vector<double> confidence;
      std::vector<neighbor_type> m_nn;
      neighbor_type* m_nun;
    private:
      size_t m_k;
      double m_max_distance;
    };

  } // namespace kNN
} //namespace Gamera

#endif