include/opencv2/flann/kmeans_index.h

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 * Copyright 2008-2009  Marius Muja (mariusm@cs.ubc.ca). All rights reserved.
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#ifndef OPENCV_FLANN_KMEANS_INDEX_H_
#define OPENCV_FLANN_KMEANS_INDEX_H_

#include <algorithm>
#include <string>
#include <map>
#include <cassert>
#include <limits>
#include <cmath>

#include "general.h"
#include "nn_index.h"
#include "dist.h"
#include "matrix.h"
#include "result_set.h"
#include "heap.h"
#include "allocator.h"
#include "random.h"
#include "saving.h"
#include "logger.h"


namespace cvflann
{

struct KMeansIndexParams : public IndexParams
{
    KMeansIndexParams(int branching = 32, int iterations = 11,
                      flann_centers_init_t centers_init = FLANN_CENTERS_RANDOM, float cb_index = 0.2 )
    {
        (*this)["algorithm"] = FLANN_INDEX_KMEANS;
        // branching factor
        (*this)["branching"] = branching;
        // max iterations to perform in one kmeans clustering (kmeans tree)
        (*this)["iterations"] = iterations;
        // algorithm used for picking the initial cluster centers for kmeans tree
        (*this)["centers_init"] = centers_init;
        // cluster boundary index. Used when searching the kmeans tree
        (*this)["cb_index"] = cb_index;
    }
};


template <typename Distance>
class KMeansIndex : public NNIndex<Distance>
{
public:
    typedef typename Distance::ElementType ElementType;
    typedef typename Distance::ResultType DistanceType;



    typedef void (KMeansIndex::* centersAlgFunction)(int, int*, int, int*, int&);

    centersAlgFunction chooseCenters;



    void chooseCentersRandom(int k, int* indices, int indices_length, int* centers, int& centers_length)
    {
        UniqueRandom r(indices_length);

        int index;
        for (index=0; index<k; ++index) {
            bool duplicate = true;
            int rnd;
            while (duplicate) {
                duplicate = false;
                rnd = r.next();
                if (rnd<0) {
                    centers_length = index;
                    return;
                }

                centers[index] = indices[rnd];

                for (int j=0; j<index; ++j) {
                    DistanceType sq = distance_(dataset_[centers[index]], dataset_[centers[j]], dataset_.cols);
                    if (sq<1e-16) {
                        duplicate = true;
                    }
                }
            }
        }

        centers_length = index;
    }


    void chooseCentersGonzales(int k, int* indices, int indices_length, int* centers, int& centers_length)
    {
        int n = indices_length;

        int rnd = rand_int(n);
        assert(rnd >=0 && rnd < n);

        centers[0] = indices[rnd];

        int index;
        for (index=1; index<k; ++index) {

            int best_index = -1;
            DistanceType best_val = 0;
            for (int j=0; j<n; ++j) {
                DistanceType dist = distance_(dataset_[centers[0]],dataset_[indices[j]],dataset_.cols);
                for (int i=1; i<index; ++i) {
                    DistanceType tmp_dist = distance_(dataset_[centers[i]],dataset_[indices[j]],dataset_.cols);
                    if (tmp_dist<dist) {
                        dist = tmp_dist;
                    }
                }
                if (dist>best_val) {
                    best_val = dist;
                    best_index = j;
                }
            }
            if (best_index!=-1) {
                centers[index] = indices[best_index];
            }
            else {
                break;
            }
        }
        centers_length = index;
    }


    void chooseCentersKMeanspp(int k, int* indices, int indices_length, int* centers, int& centers_length)
    {
        int n = indices_length;

        double currentPot = 0;
        DistanceType* closestDistSq = new DistanceType[n];

        // Choose one random center and set the closestDistSq values
        int index = rand_int(n);
        assert(index >=0 && index < n);
        centers[0] = indices[index];

        for (int i = 0; i < n; i++) {
            closestDistSq[i] = distance_(dataset_[indices[i]], dataset_[indices[index]], dataset_.cols);
            currentPot += closestDistSq[i];
        }


        const int numLocalTries = 1;

        // Choose each center
        int centerCount;
        for (centerCount = 1; centerCount < k; centerCount++) {

            // Repeat several trials
            double bestNewPot = -1;
            int bestNewIndex = -1;
            for (int localTrial = 0; localTrial < numLocalTries; localTrial++) {

                // Choose our center - have to be slightly careful to return a valid answer even accounting
                // for possible rounding errors
                double randVal = rand_double(currentPot);
                for (index = 0; index < n-1; index++) {
                    if (randVal <= closestDistSq[index]) break;
                    else randVal -= closestDistSq[index];
                }

                // Compute the new potential
                double newPot = 0;
                for (int i = 0; i < n; i++) newPot += std::min( distance_(dataset_[indices[i]], dataset_[indices[index]], dataset_.cols), closestDistSq[i] );

                // Store the best result
                if ((bestNewPot < 0)||(newPot < bestNewPot)) {
                    bestNewPot = newPot;
                    bestNewIndex = index;
                }
            }

            // Add the appropriate center
            centers[centerCount] = indices[bestNewIndex];
            currentPot = bestNewPot;
            for (int i = 0; i < n; i++) closestDistSq[i] = std::min( distance_(dataset_[indices[i]], dataset_[indices[bestNewIndex]], dataset_.cols), closestDistSq[i] );
        }

        centers_length = centerCount;

        delete[] closestDistSq;
    }



public:

    flann_algorithm_t getType() const
    {
        return FLANN_INDEX_KMEANS;
    }

    KMeansIndex(const Matrix<ElementType>& inputData, const IndexParams& params = KMeansIndexParams(),
                Distance d = Distance())
        : dataset_(inputData), index_params_(params), root_(NULL), indices_(NULL), distance_(d)
    {
        memoryCounter_ = 0;

        size_ = dataset_.rows;
        veclen_ = dataset_.cols;

        branching_ = get_param(params,"branching",32);
        iterations_ = get_param(params,"iterations",11);
        if (iterations_<0) {
            iterations_ = (std::numeric_limits<int>::max)();
        }
        centers_init_  = get_param(params,"centers_init",FLANN_CENTERS_RANDOM);

        if (centers_init_==FLANN_CENTERS_RANDOM) {
            chooseCenters = &KMeansIndex::chooseCentersRandom;
        }
        else if (centers_init_==FLANN_CENTERS_GONZALES) {
            chooseCenters = &KMeansIndex::chooseCentersGonzales;
        }
        else if (centers_init_==FLANN_CENTERS_KMEANSPP) {
            chooseCenters = &KMeansIndex::chooseCentersKMeanspp;
        }
        else {
            throw FLANNException("Unknown algorithm for choosing initial centers.");
        }
        cb_index_ = 0.4f;

    }


    KMeansIndex(const KMeansIndex&);
    KMeansIndex& operator=(const KMeansIndex&);


    virtual ~KMeansIndex()
    {
        if (root_ != NULL) {
            free_centers(root_);
        }
        if (indices_!=NULL) {
            delete[] indices_;
        }
    }

    size_t size() const
    {
        return size_;
    }

    size_t veclen() const
    {
        return veclen_;
    }


    void set_cb_index( float index)
    {
        cb_index_ = index;
    }

    int usedMemory() const
    {
        return pool_.usedMemory+pool_.wastedMemory+memoryCounter_;
    }

    void buildIndex()
    {
        if (branching_<2) {
            throw FLANNException("Branching factor must be at least 2");
        }

        indices_ = new int[size_];
        for (size_t i=0; i<size_; ++i) {
            indices_[i] = int(i);
        }

        root_ = pool_.allocate<KMeansNode>();
        computeNodeStatistics(root_, indices_, (int)size_);
        computeClustering(root_, indices_, (int)size_, branching_,0);
    }


    void saveIndex(FILE* stream)
    {
        save_value(stream, branching_);
        save_value(stream, iterations_);
        save_value(stream, memoryCounter_);
        save_value(stream, cb_index_);
        save_value(stream, *indices_, (int)size_);

        save_tree(stream, root_);
    }


    void loadIndex(FILE* stream)
    {
        load_value(stream, branching_);
        load_value(stream, iterations_);
        load_value(stream, memoryCounter_);
        load_value(stream, cb_index_);
        if (indices_!=NULL) {
            delete[] indices_;
        }
        indices_ = new int[size_];
        load_value(stream, *indices_, size_);

        if (root_!=NULL) {
            free_centers(root_);
        }
        load_tree(stream, root_);

        index_params_["algorithm"] = getType();
        index_params_["branching"] = branching_;
        index_params_["iterations"] = iterations_;
        index_params_["centers_init"] = centers_init_;
        index_params_["cb_index"] = cb_index_;

    }


    void findNeighbors(ResultSet<DistanceType>& result, const ElementType* vec, const SearchParams& searchParams)
    {

        int maxChecks = get_param(searchParams,"checks",32);

        if (maxChecks==FLANN_CHECKS_UNLIMITED) {
            findExactNN(root_, result, vec);
        }
        else {
            // Priority queue storing intermediate branches in the best-bin-first search
            Heap<BranchSt>* heap = new Heap<BranchSt>((int)size_);

            int checks = 0;
            findNN(root_, result, vec, checks, maxChecks, heap);

            BranchSt branch;
            while (heap->popMin(branch) && (checks<maxChecks || !result.full())) {
                KMeansNodePtr node = branch.node;
                findNN(node, result, vec, checks, maxChecks, heap);
            }
            assert(result.full());

            delete heap;
        }

    }

    int getClusterCenters(Matrix<DistanceType>& centers)
    {
        int numClusters = centers.rows;
        if (numClusters<1) {
            throw FLANNException("Number of clusters must be at least 1");
        }

        DistanceType variance;
        KMeansNodePtr* clusters = new KMeansNodePtr[numClusters];

        int clusterCount = getMinVarianceClusters(root_, clusters, numClusters, variance);

        Logger::info("Clusters requested: %d, returning %d\n",numClusters, clusterCount);

        for (int i=0; i<clusterCount; ++i) {
            DistanceType* center = clusters[i]->pivot;
            for (size_t j=0; j<veclen_; ++j) {
                centers[i][j] = center[j];
            }
        }
        delete[] clusters;

        return clusterCount;
    }

    IndexParams getParameters() const
    {
        return index_params_;
    }


private:
    struct KMeansNode
    {
        DistanceType* pivot;
        DistanceType radius;
        DistanceType mean_radius;
        DistanceType variance;
        int size;
        KMeansNode** childs;
        int* indices;
        int level;
    };
    typedef KMeansNode* KMeansNodePtr;

    typedef BranchStruct<KMeansNodePtr, DistanceType> BranchSt;




    void save_tree(FILE* stream, KMeansNodePtr node)
    {
        save_value(stream, *node);
        save_value(stream, *(node->pivot), (int)veclen_);
        if (node->childs==NULL) {
            int indices_offset = (int)(node->indices - indices_);
            save_value(stream, indices_offset);
        }
        else {
            for(int i=0; i<branching_; ++i) {
                save_tree(stream, node->childs[i]);
            }
        }
    }


    void load_tree(FILE* stream, KMeansNodePtr& node)
    {
        node = pool_.allocate<KMeansNode>();
        load_value(stream, *node);
        node->pivot = new DistanceType[veclen_];
        load_value(stream, *(node->pivot), (int)veclen_);
        if (node->childs==NULL) {
            int indices_offset;
            load_value(stream, indices_offset);
            node->indices = indices_ + indices_offset;
        }
        else {
            node->childs = pool_.allocate<KMeansNodePtr>(branching_);
            for(int i=0; i<branching_; ++i) {
                load_tree(stream, node->childs[i]);
            }
        }
    }


    void free_centers(KMeansNodePtr node)
    {
        delete[] node->pivot;
        if (node->childs!=NULL) {
            for (int k=0; k<branching_; ++k) {
                free_centers(node->childs[k]);
            }
        }
    }

    void computeNodeStatistics(KMeansNodePtr node, int* indices, int indices_length)
    {

        DistanceType radius = 0;
        DistanceType variance = 0;
        DistanceType* mean = new DistanceType[veclen_];
        memoryCounter_ += int(veclen_*sizeof(DistanceType));

        memset(mean,0,veclen_*sizeof(DistanceType));

        for (size_t i=0; i<size_; ++i) {
            ElementType* vec = dataset_[indices[i]];
            for (size_t j=0; j<veclen_; ++j) {
                mean[j] += vec[j];
            }
            variance += distance_(vec, ZeroIterator<ElementType>(), veclen_);
        }
        for (size_t j=0; j<veclen_; ++j) {
            mean[j] /= size_;
        }
        variance /= size_;
        variance -= distance_(mean, ZeroIterator<ElementType>(), veclen_);

        DistanceType tmp = 0;
        for (int i=0; i<indices_length; ++i) {
            tmp = distance_(mean, dataset_[indices[i]], veclen_);
            if (tmp>radius) {
                radius = tmp;
            }
        }

        node->variance = variance;
        node->radius = radius;
        node->pivot = mean;
    }


    void computeClustering(KMeansNodePtr node, int* indices, int indices_length, int branching, int level)
    {
        node->size = indices_length;
        node->level = level;

        if (indices_length < branching) {
            node->indices = indices;
            std::sort(node->indices,node->indices+indices_length);
            node->childs = NULL;
            return;
        }

        int* centers_idx = new int[branching];
        int centers_length;
        (this->*chooseCenters)(branching, indices, indices_length, centers_idx, centers_length);

        if (centers_length<branching) {
            node->indices = indices;
            std::sort(node->indices,node->indices+indices_length);
            node->childs = NULL;
            delete [] centers_idx;
            return;
        }


        Matrix<double> dcenters(new double[branching*veclen_],branching,veclen_);
        for (int i=0; i<centers_length; ++i) {
            ElementType* vec = dataset_[centers_idx[i]];
            for (size_t k=0; k<veclen_; ++k) {
                dcenters[i][k] = double(vec[k]);
            }
        }
        delete[] centers_idx;

        std::vector<DistanceType> radiuses(branching);
        int* count = new int[branching];
        for (int i=0; i<branching; ++i) {
            radiuses[i] = 0;
            count[i] = 0;
        }

        //  assign points to clusters
        int* belongs_to = new int[indices_length];
        for (int i=0; i<indices_length; ++i) {

            DistanceType sq_dist = distance_(dataset_[indices[i]], dcenters[0], veclen_);
            belongs_to[i] = 0;
            for (int j=1; j<branching; ++j) {
                DistanceType new_sq_dist = distance_(dataset_[indices[i]], dcenters[j], veclen_);
                if (sq_dist>new_sq_dist) {
                    belongs_to[i] = j;
                    sq_dist = new_sq_dist;
                }
            }
            if (sq_dist>radiuses[belongs_to[i]]) {
                radiuses[belongs_to[i]] = sq_dist;
            }
            count[belongs_to[i]]++;
        }

        bool converged = false;
        int iteration = 0;
        while (!converged && iteration<iterations_) {
            converged = true;
            iteration++;

            // compute the new cluster centers
            for (int i=0; i<branching; ++i) {
                memset(dcenters[i],0,sizeof(double)*veclen_);
                radiuses[i] = 0;
            }
            for (int i=0; i<indices_length; ++i) {
                ElementType* vec = dataset_[indices[i]];
                double* center = dcenters[belongs_to[i]];
                for (size_t k=0; k<veclen_; ++k) {
                    center[k] += vec[k];
                }
            }
            for (int i=0; i<branching; ++i) {
                int cnt = count[i];
                for (size_t k=0; k<veclen_; ++k) {
                    dcenters[i][k] /= cnt;
                }
            }

            // reassign points to clusters
            for (int i=0; i<indices_length; ++i) {
                DistanceType sq_dist = distance_(dataset_[indices[i]], dcenters[0], veclen_);
                int new_centroid = 0;
                for (int j=1; j<branching; ++j) {
                    DistanceType new_sq_dist = distance_(dataset_[indices[i]], dcenters[j], veclen_);
                    if (sq_dist>new_sq_dist) {
                        new_centroid = j;
                        sq_dist = new_sq_dist;
                    }
                }
                if (sq_dist>radiuses[new_centroid]) {
                    radiuses[new_centroid] = sq_dist;
                }
                if (new_centroid != belongs_to[i]) {
                    count[belongs_to[i]]--;
                    count[new_centroid]++;
                    belongs_to[i] = new_centroid;

                    converged = false;
                }
            }

            for (int i=0; i<branching; ++i) {
                // if one cluster converges to an empty cluster,
                // move an element into that cluster
                if (count[i]==0) {
                    int j = (i+1)%branching;
                    while (count[j]<=1) {
                        j = (j+1)%branching;
                    }

                    for (int k=0; k<indices_length; ++k) {
                        if (belongs_to[k]==j) {
                            belongs_to[k] = i;
                            count[j]--;
                            count[i]++;
                            break;
                        }
                    }
                    converged = false;
                }
            }

        }

        DistanceType** centers = new DistanceType*[branching];

        for (int i=0; i<branching; ++i) {
            centers[i] = new DistanceType[veclen_];
            memoryCounter_ += (int)(veclen_*sizeof(DistanceType));
            for (size_t k=0; k<veclen_; ++k) {
                centers[i][k] = (DistanceType)dcenters[i][k];
            }
        }


        // compute kmeans clustering for each of the resulting clusters
        node->childs = pool_.allocate<KMeansNodePtr>(branching);
        int start = 0;
        int end = start;
        for (int c=0; c<branching; ++c) {
            int s = count[c];

            DistanceType variance = 0;
            DistanceType mean_radius =0;
            for (int i=0; i<indices_length; ++i) {
                if (belongs_to[i]==c) {
                    DistanceType d = distance_(dataset_[indices[i]], ZeroIterator<ElementType>(), veclen_);
                    variance += d;
                    mean_radius += sqrt(d);
                    std::swap(indices[i],indices[end]);
                    std::swap(belongs_to[i],belongs_to[end]);
                    end++;
                }
            }
            variance /= s;
            mean_radius /= s;
            variance -= distance_(centers[c], ZeroIterator<ElementType>(), veclen_);

            node->childs[c] = pool_.allocate<KMeansNode>();
            node->childs[c]->radius = radiuses[c];
            node->childs[c]->pivot = centers[c];
            node->childs[c]->variance = variance;
            node->childs[c]->mean_radius = mean_radius;
            node->childs[c]->indices = NULL;
            computeClustering(node->childs[c],indices+start, end-start, branching, level+1);
            start=end;
        }

        delete[] dcenters.data;
        delete[] centers;
        delete[] count;
        delete[] belongs_to;
    }



    void findNN(KMeansNodePtr node, ResultSet<DistanceType>& result, const ElementType* vec, int& checks, int maxChecks,
                Heap<BranchSt>* heap)
    {
        // Ignore those clusters that are too far away
        {
            DistanceType bsq = distance_(vec, node->pivot, veclen_);
            DistanceType rsq = node->radius;
            DistanceType wsq = result.worstDist();

            DistanceType val = bsq-rsq-wsq;
            DistanceType val2 = val*val-4*rsq*wsq;

            //if (val>0) {
            if ((val>0)&&(val2>0)) {
                return;
            }
        }

        if (node->childs==NULL) {
            if (checks>=maxChecks) {
                if (result.full()) return;
            }
            checks += node->size;
            for (int i=0; i<node->size; ++i) {
                int index = node->indices[i];
                DistanceType dist = distance_(dataset_[index], vec, veclen_);
                result.addPoint(dist, index);
            }
        }
        else {
            DistanceType* domain_distances = new DistanceType[branching_];
            int closest_center = exploreNodeBranches(node, vec, domain_distances, heap);
            delete[] domain_distances;
            findNN(node->childs[closest_center],result,vec, checks, maxChecks, heap);
        }
    }

    int exploreNodeBranches(KMeansNodePtr node, const ElementType* q, DistanceType* domain_distances, Heap<BranchSt>* heap)
    {

        int best_index = 0;
        domain_distances[best_index] = distance_(q, node->childs[best_index]->pivot, veclen_);
        for (int i=1; i<branching_; ++i) {
            domain_distances[i] = distance_(q, node->childs[i]->pivot, veclen_);
            if (domain_distances[i]<domain_distances[best_index]) {
                best_index = i;
            }
        }

        //      float* best_center = node->childs[best_index]->pivot;
        for (int i=0; i<branching_; ++i) {
            if (i != best_index) {
                domain_distances[i] -= cb_index_*node->childs[i]->variance;

                //              float dist_to_border = getDistanceToBorder(node.childs[i].pivot,best_center,q);
                //              if (domain_distances[i]<dist_to_border) {
                //                  domain_distances[i] = dist_to_border;
                //              }
                heap->insert(BranchSt(node->childs[i],domain_distances[i]));
            }
        }

        return best_index;
    }


    void findExactNN(KMeansNodePtr node, ResultSet<DistanceType>& result, const ElementType* vec)
    {
        // Ignore those clusters that are too far away
        {
            DistanceType bsq = distance_(vec, node->pivot, veclen_);
            DistanceType rsq = node->radius;
            DistanceType wsq = result.worstDist();

            DistanceType val = bsq-rsq-wsq;
            DistanceType val2 = val*val-4*rsq*wsq;

            //                  if (val>0) {
            if ((val>0)&&(val2>0)) {
                return;
            }
        }


        if (node->childs==NULL) {
            for (int i=0; i<node->size; ++i) {
                int index = node->indices[i];
                DistanceType dist = distance_(dataset_[index], vec, veclen_);
                result.addPoint(dist, index);
            }
        }
        else {
            int* sort_indices = new int[branching_];

            getCenterOrdering(node, vec, sort_indices);

            for (int i=0; i<branching_; ++i) {
                findExactNN(node->childs[sort_indices[i]],result,vec);
            }

            delete[] sort_indices;
        }
    }


    void getCenterOrdering(KMeansNodePtr node, const ElementType* q, int* sort_indices)
    {
        DistanceType* domain_distances = new DistanceType[branching_];
        for (int i=0; i<branching_; ++i) {
            DistanceType dist = distance_(q, node->childs[i]->pivot, veclen_);

            int j=0;
            while (domain_distances[j]<dist && j<i) j++;
            for (int k=i; k>j; --k) {
                domain_distances[k] = domain_distances[k-1];
                sort_indices[k] = sort_indices[k-1];
            }
            domain_distances[j] = dist;
            sort_indices[j] = i;
        }
        delete[] domain_distances;
    }

    DistanceType getDistanceToBorder(DistanceType* p, DistanceType* c, DistanceType* q)
    {
        DistanceType sum = 0;
        DistanceType sum2 = 0;

        for (int i=0; i<veclen_; ++i) {
            DistanceType t = c[i]-p[i];
            sum += t*(q[i]-(c[i]+p[i])/2);
            sum2 += t*t;
        }

        return sum*sum/sum2;
    }


    int getMinVarianceClusters(KMeansNodePtr root, KMeansNodePtr* clusters, int clusters_length, DistanceType& varianceValue)
    {
        int clusterCount = 1;
        clusters[0] = root;

        DistanceType meanVariance = root->variance*root->size;

        while (clusterCount<clusters_length) {
            DistanceType minVariance = (std::numeric_limits<DistanceType>::max)();
            int splitIndex = -1;

            for (int i=0; i<clusterCount; ++i) {
                if (clusters[i]->childs != NULL) {

                    DistanceType variance = meanVariance - clusters[i]->variance*clusters[i]->size;

                    for (int j=0; j<branching_; ++j) {
                        variance += clusters[i]->childs[j]->variance*clusters[i]->childs[j]->size;
                    }
                    if (variance<minVariance) {
                        minVariance = variance;
                        splitIndex = i;
                    }
                }
            }

            if (splitIndex==-1) break;
            if ( (branching_+clusterCount-1) > clusters_length) break;

            meanVariance = minVariance;

            // split node
            KMeansNodePtr toSplit = clusters[splitIndex];
            clusters[splitIndex] = toSplit->childs[0];
            for (int i=1; i<branching_; ++i) {
                clusters[clusterCount++] = toSplit->childs[i];
            }
        }

        varianceValue = meanVariance/root->size;
        return clusterCount;
    }

private:
    int branching_;

    int iterations_;

    flann_centers_init_t centers_init_;

    float cb_index_;

    const Matrix<ElementType> dataset_;

    IndexParams index_params_;

    size_t size_;

    size_t veclen_;

    KMeansNodePtr root_;

    int* indices_;

    Distance distance_;

    PooledAllocator pool_;

    int memoryCounter_;
};

}

#endif //OPENCV_FLANN_KMEANS_INDEX_H_