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vptree.hpp
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vptree.hpp
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// Based on http://stevehanov.ca/blog/index.php?id=130 by Steve Hanov
#pragma once
#include <algorithm>
#include <vector>
#include <queue>
#include <limits>
#include <random>
#include <cmath>
#include <stdexcept>
namespace vpt {
typedef std::vector<double> Vector;
typedef std::function<double(const Vector& v1, const Vector& v2)> Metric;
typedef std::pair<std::vector<double>, std::vector<int>> DistancesIndices;
typedef std::pair<std::vector<std::vector<double>>, std::vector<std::vector<int>>> BatchDistancesIndices;
template<class InputIterator>
double sum(InputIterator begin, InputIterator end) {
double result = 0;
for (; begin != end; ++begin) {
result += *begin;
}
return result;
}
template<typename Container>
struct EuclideanMetric {
double operator() (const Container& v1, const Container& v2) const {
Vector diffSquares(v1.size());
std::transform(v1.begin(), v1.end(), v2.begin(), diffSquares.begin(), [] (double lhs, double rhs) {
return (lhs - rhs) * (lhs - rhs);
});
auto sum = vpt::sum(diffSquares.begin(), diffSquares.end());
return std::sqrt(sum);
}
};
class DimensionMismatch: public std::runtime_error {
public:
DimensionMismatch(int expected, int got)
: std::runtime_error("Item dimension doesn't match: expected " + std::to_string(expected) + ", got " + std::to_string(got))
{}
};
class Searcher;
class VpTree {
public:
template<typename InputIterator>
explicit VpTree(InputIterator start, InputIterator end, Metric metric = EuclideanMetric<Vector>());
template<typename Container>
explicit VpTree(const Container& container, Metric metric = EuclideanMetric<Vector>());
explicit VpTree(std::initializer_list<Vector> list, Metric metric = EuclideanMetric<Vector>());
DistancesIndices getNearestNeighbors(const Vector& target, int neighborsCount) const;
template<typename VectorLike>
DistancesIndices getNearestNeighbors(const VectorLike& target, int neighborsCount) const;
DistancesIndices getNearestNeighbors(std::initializer_list<double> target, int neighborsCount) const;
template<typename Container>
BatchDistancesIndices getNearestNeighborsBatch(const Container& targets, int neighborsCount) const;
BatchDistancesIndices getNearestNeighborsBatch(std::initializer_list<Vector> targets, int neighborsCount) const;
const Metric getDistance;
private:
struct Node {
static const int Leaf = -1;
Node(int item, double threshold = 0., int left = Leaf, int right = Leaf)
: item(item), threshold(threshold), left(left), right(right)
{ }
int item;
double threshold;
int left;
int right;
};
private:
typedef std::pair<Vector, int> Item;
std::vector<Item> items_;
std::vector<Node> nodes_;
std::mt19937 rng_;
int dimension_;
private:
template<typename InputIterator>
std::vector<Item> makeItems(InputIterator start, InputIterator end);
int makeTree(int lower, int upper);
void selectRoot(int lower, int upper);
void partitionByDistance(int lower, int pos, int upper);
int makeNode(int item);
Node root() const { return nodes_[0]; }
friend class Searcher;
};
class Searcher {
private:
typedef typename VpTree::Node Node;
public:
explicit Searcher(const VpTree* tree, const Vector& target, int neighborsCount);
std::pair<std::vector<double>, std::vector<int>> search();
struct HeapItem {
bool operator < (const HeapItem& other) const {
return dist < other.dist;
}
int item;
double dist;
};
private:
void searchInNode(const Node& node);
const VpTree* tree_;
Vector target_;
int neighborsCount_;
double tau_;
std::priority_queue<HeapItem> heap_;
};
template<typename InputIterator>
VpTree::VpTree(InputIterator start, InputIterator end, Metric metric)
: getDistance(metric), items_(makeItems(start, end)), nodes_(), rng_() {
std::random_device rd;
rng_.seed(rd());
nodes_.reserve(items_.size());
makeTree(0, items_.size());
}
template<typename Container>
VpTree::VpTree(const Container& container, Metric metric)
: VpTree(container.begin(), container.end(), metric)
{ }
VpTree::VpTree(std::initializer_list<Vector> list, Metric metric)
: VpTree(list.begin(), list.end(), metric)
{ }
int VpTree::makeTree(int lower, int upper) {
if (lower >= upper) {
return Node::Leaf;
} else if (lower + 1 == upper) {
return makeNode(lower);
} else {
selectRoot(lower, upper);
int median = (upper + lower) / 2;
partitionByDistance(lower, median, upper);
auto node = makeNode(lower);
nodes_[node].threshold = getDistance(items_[lower].first, items_[median].first);
nodes_[node].left = makeTree(lower + 1, median);
nodes_[node].right = makeTree(median, upper);
return node;
}
}
void VpTree::selectRoot(int lower, int upper) {
std::uniform_int_distribution<int> uni(lower, upper - 1);
int root = uni(rng_);
std::swap(items_[lower], items_[root]);
}
void VpTree::partitionByDistance(int lower, int pos, int upper) {
std::nth_element(
items_.begin() + lower + 1,
items_.begin() + pos,
items_.begin() + upper,
[lower, this] (const Item& i1, const Item& i2) {
return getDistance(items_[lower].first, i1.first) < getDistance(items_[lower].first, i2.first);
});
}
int VpTree::makeNode(int item) {
nodes_.push_back(Node(item));
return nodes_.size() - 1;
}
template<typename InputIterator>
std::vector<std::pair<Vector, int>> VpTree::makeItems(InputIterator begin, InputIterator end) {
if (begin != end) {
dimension_ = begin->size();
} else {
dimension_ = -1;
}
std::vector<Item> res;
for (int i = 0; begin != end; ++begin, ++i) {
auto vec = Vector(begin->begin(), begin->end());
res.push_back(std::make_pair(vec, i));
auto lastDimension = res.back().first.size();
if (lastDimension != dimension_) {
throw DimensionMismatch(dimension_, lastDimension);
}
}
return res;
}
template<typename VectorLike>
DistancesIndices VpTree::getNearestNeighbors(const VectorLike& target, int neighborsCount) const {
return getNearestNeighbors(Vector(target.begin(), target.end()), neighborsCount);
}
DistancesIndices VpTree::getNearestNeighbors(std::initializer_list<double> target, int neighborsCount) const {
return getNearestNeighbors(Vector(target.begin(), target.end()), neighborsCount);
}
DistancesIndices VpTree::getNearestNeighbors(const Vector& target, int neighborsCount) const {
auto targetDimension = target.size();
if (targetDimension != dimension_) {
throw DimensionMismatch(dimension_, targetDimension);
}
Searcher searcher(this, target, neighborsCount);
return searcher.search();
}
template<typename Container>
BatchDistancesIndices VpTree::getNearestNeighborsBatch(const Container& targets, int neighborsCount) const {
std::vector<std::vector<double>> batchDistances(targets.size());
std::vector<std::vector<int>> batchIndices(targets.size());
#pragma omp parallel for schedule(dynamic)
for (int i = 0; i < targets.size(); ++i) {
std::tie(batchDistances[i], batchIndices[i]) = getNearestNeighbors(targets[i], neighborsCount);
}
return BatchDistancesIndices(batchDistances, batchIndices);
}
BatchDistancesIndices VpTree::getNearestNeighborsBatch(std::initializer_list<Vector> targets, int neighborsCount) const {
return getNearestNeighborsBatch(std::vector<Vector>(targets.begin(), targets.end()), neighborsCount);
}
Searcher::Searcher(const VpTree* tree, const Vector& target, int neighborsCount)
: tree_(tree), target_(target), neighborsCount_(neighborsCount), tau_(std::numeric_limits<double>::max()), heap_()
{ }
DistancesIndices Searcher::search() {
searchInNode(tree_->root());
DistancesIndices results;
while(!heap_.empty()) {
results.first.push_back(heap_.top().dist);
results.second.push_back(tree_->items_[heap_.top().item].second);
heap_.pop();
}
std::reverse(results.first.begin(), results.first.end());
std::reverse(results.second.begin(), results.second.end());
return results;
}
void Searcher::searchInNode(const Node& node) {
double dist = tree_->getDistance(tree_->items_[node.item].first, target_);
if (dist < tau_) {
if (heap_.size() == neighborsCount_)
heap_.pop();
heap_.push(HeapItem{node.item, dist});
if (heap_.size() == neighborsCount_)
tau_ = heap_.top().dist;
}
if (dist < node.threshold) {
if (node.left != Node::Leaf && dist - tau_ <= node.threshold)
searchInNode(tree_->nodes_[node.left]);
if (node.right != Node::Leaf && dist + tau_ >= node.threshold)
searchInNode(tree_->nodes_[node.right]);
} else {
if (node.right != Node::Leaf && dist + tau_ >= node.threshold)
searchInNode(tree_->nodes_[node.right]);
if (node.left != Node::Leaf && dist - tau_ <= node.threshold)
searchInNode(tree_->nodes_[node.left]);
}
}
}