DTBStat(const TreeType& node) :
maxNeighborDistance(DBL_MAX),
minNeighborDistance(DBL_MAX),
bound(DBL_MAX),
componentMembership(
((node.NumPoints() == 1) && (node.NumChildren() == 0)) ?
node.Point(0) : -1) { }
void NeighborSearchRules<
SortPolicy,
MetricType,
TreeType>::
UpdateAfterRecursion(TreeType& queryNode, TreeType& /* referenceNode */)
{
// Find the worst distance that the children found (including any points), and
// update the bound accordingly.
double worstDistance = SortPolicy::BestDistance();
// First look through children nodes.
for (size_t i = 0; i < queryNode.NumChildren(); ++i)
{
if (SortPolicy::IsBetter(worstDistance, queryNode.Child(i).Stat().Bound()))
worstDistance = queryNode.Child(i).Stat().Bound();
}
// Now look through children points.
for (size_t i = 0; i < queryNode.NumPoints(); ++i)
{
if (SortPolicy::IsBetter(worstDistance,
distances(distances.n_rows - 1, queryNode.Point(i))))
worstDistance = distances(distances.n_rows - 1, queryNode.Point(i));
}
// Take the worst distance from all of these, and update our bound to reflect
// that.
queryNode.Stat().Bound() = worstDistance;
}
DualTreeKMeansStatistic(TreeType& node) :
neighbor::NeighborSearchStat<neighbor::NearestNeighborSort>(),
upperBound(DBL_MAX),
lowerBound(DBL_MAX),
owner(size_t(-1)),
pruned(size_t(-1)),
staticPruned(false),
staticUpperBoundMovement(0.0),
staticLowerBoundMovement(0.0),
trueParent(node.Parent())
{
// Empirically calculate the centroid.
centroid.zeros(node.Dataset().n_rows);
for (size_t i = 0; i < node.NumPoints(); ++i)
{
// Correct handling of cover tree: don't double-count the point which
// appears in the children.
if (tree::TreeTraits<TreeType>::HasSelfChildren && i == 0 &&
node.NumChildren() > 0)
continue;
centroid += node.Dataset().col(node.Point(i));
}
for (size_t i = 0; i < node.NumChildren(); ++i)
centroid += node.Child(i).NumDescendants() *
node.Child(i).Stat().Centroid();
centroid /= node.NumDescendants();
// Set the true children correctly.
trueChildren.resize(node.NumChildren());
for (size_t i = 0; i < node.NumChildren(); ++i)
trueChildren[i] = &node.Child(i);
}
void GreedySingleTreeTraverser<TreeType, RuleType>::Traverse(
const size_t queryIndex,
TreeType& referenceNode)
{
// Run the base case as necessary for all the points in the reference node.
for (size_t i = 0; i < referenceNode.NumPoints(); ++i)
rule.BaseCase(queryIndex, referenceNode.Point(i));
size_t bestChild = rule.GetBestChild(queryIndex, referenceNode);
size_t numDescendants;
// Check that referencenode is not a leaf node while calculating number of
// descendants of it's best child.
if (!referenceNode.IsLeaf())
numDescendants = referenceNode.Child(bestChild).NumDescendants();
else
numDescendants = referenceNode.NumPoints();
// If number of descendants are more than minBaseCases than we can go along
// with best child otherwise we need to traverse for each descendant to
// ensure that we calculate at least minBaseCases number of base cases.
if (!referenceNode.IsLeaf())
{
if (numDescendants > minBaseCases)
{
// We are prunning all but one child.
numPrunes += referenceNode.NumChildren() - 1;
// Recurse the best child.
Traverse(queryIndex, referenceNode.Child(bestChild));
}
else
{
// Run the base case over first minBaseCases number of descendants.
for (size_t i = 0; i <= minBaseCases; ++i)
rule.BaseCase(queryIndex, referenceNode.Descendant(i));
}
}
}
inline double DTBRules<MetricType, TreeType>::CalculateBound(
TreeType& queryNode) const
{
double worstPointBound = -DBL_MAX;
double bestPointBound = DBL_MAX;
double worstChildBound = -DBL_MAX;
double bestChildBound = DBL_MAX;
// Now, find the best and worst point bounds.
for (size_t i = 0; i < queryNode.NumPoints(); ++i)
{
const size_t pointComponent = connections.Find(queryNode.Point(i));
const double bound = neighborsDistances[pointComponent];
if (bound > worstPointBound)
worstPointBound = bound;
if (bound < bestPointBound)
bestPointBound = bound;
}
// Find the best and worst child bounds.
for (size_t i = 0; i < queryNode.NumChildren(); ++i)
{
const double maxBound = queryNode.Child(i).Stat().MaxNeighborDistance();
if (maxBound > worstChildBound)
worstChildBound = maxBound;
const double minBound = queryNode.Child(i).Stat().MinNeighborDistance();
if (minBound < bestChildBound)
bestChildBound = minBound;
}
// Now calculate the actual bounds.
const double worstBound = std::max(worstPointBound, worstChildBound);
const double bestBound = std::min(bestPointBound, bestChildBound);
// We must check that bestBound != DBL_MAX; otherwise, we risk overflow.
const double bestAdjustedBound = (bestBound == DBL_MAX) ? DBL_MAX :
bestBound + 2 * queryNode.FurthestDescendantDistance();
// Update the relevant quantities in the node.
queryNode.Stat().MaxNeighborDistance() = worstBound;
queryNode.Stat().MinNeighborDistance() = bestBound;
queryNode.Stat().Bound() = std::min(worstBound, bestAdjustedBound);
return queryNode.Stat().Bound();
}
DualTreeKMeansStatistic(TreeType& node) :
closestQueryNode(NULL),
minQueryNodeDistance(DBL_MAX),
maxQueryNodeDistance(DBL_MAX),
clustersPruned(0),
iteration(size_t() - 1)
{
// Empirically calculate the centroid.
centroid.zeros(node.Dataset().n_rows);
for (size_t i = 0; i < node.NumPoints(); ++i)
centroid += node.Dataset().col(node.Point(i));
for (size_t i = 0; i < node.NumChildren(); ++i)
centroid += node.Child(i).NumDescendants() *
node.Child(i).Stat().Centroid();
centroid /= node.NumDescendants();
}
PellegMooreKMeansStatistic(TreeType& node)
{
centroid.zeros(node.Dataset().n_rows);
// Hope it's a depth-first build procedure. Also, this won't work right for
// trees that have self-children or stuff like that.
for (size_t i = 0; i < node.NumChildren(); ++i)
{
centroid += node.Child(i).NumDescendants() *
node.Child(i).Stat().Centroid();
}
for (size_t i = 0; i < node.NumPoints(); ++i)
{
centroid += node.Dataset().col(node.Point(i));
}
if (node.NumDescendants() > 0)
centroid /= node.NumDescendants();
else
centroid.fill(DBL_MAX); // Invalid centroid. What else can we do?
}
double PellegMooreKMeansRules<MetricType, TreeType>::Score(
const size_t /* queryIndex */,
TreeType& referenceNode)
{
// Obtain the parent's blacklist. If this is the root node, we'll start with
// an empty blacklist. This means that after each iteration, we don't need to
// reset any statistics.
if (referenceNode.Parent() == NULL ||
referenceNode.Parent()->Stat().Blacklist().n_elem == 0)
referenceNode.Stat().Blacklist().zeros(centroids.n_cols);
else
referenceNode.Stat().Blacklist() =
referenceNode.Parent()->Stat().Blacklist();
// The query index is a fake index that we won't use, and the reference node
// holds all of the points in the dataset. Our goal is to determine whether
// or not this node is dominated by a single cluster.
const size_t whitelisted = centroids.n_cols -
arma::accu(referenceNode.Stat().Blacklist());
distanceCalculations += whitelisted;
// Which cluster has minimum distance to the node?
size_t closestCluster = centroids.n_cols;
double minMinDistance = DBL_MAX;
for (size_t i = 0; i < centroids.n_cols; ++i)
{
if (referenceNode.Stat().Blacklist()[i] == 0)
{
const double minDistance = referenceNode.MinDistance(centroids.col(i));
if (minDistance < minMinDistance)
{
minMinDistance = minDistance;
closestCluster = i;
}
}
}
// Now, for every other whitelisted cluster, determine if the closest cluster
// owns the point. This calculation is specific to hyperrectangle trees (but,
// this implementation is specific to kd-trees, so that's okay). For
// circular-bound trees, the condition should be simpler and can probably be
// expressed as a comparison between minimum and maximum distances.
size_t newBlacklisted = 0;
for (size_t c = 0; c < centroids.n_cols; ++c)
{
if (referenceNode.Stat().Blacklist()[c] == 1 || c == closestCluster)
continue;
// This algorithm comes from the proof of Lemma 4 in the extended version
// of the Pelleg-Moore paper (the CMU tech report, that is). It has been
// adapted for speed.
arma::vec cornerPoint(centroids.n_rows);
for (size_t d = 0; d < referenceNode.Bound().Dim(); ++d)
{
if (centroids(d, c) > centroids(d, closestCluster))
cornerPoint(d) = referenceNode.Bound()[d].Hi();
else
cornerPoint(d) = referenceNode.Bound()[d].Lo();
}
const double closestDist = metric.Evaluate(cornerPoint,
centroids.col(closestCluster));
const double otherDist = metric.Evaluate(cornerPoint, centroids.col(c));
distanceCalculations += 3; // One for cornerPoint, then two distances.
if (closestDist < otherDist)
{
// The closest cluster dominates the node with respect to the cluster c.
// So we can blacklist c.
referenceNode.Stat().Blacklist()[c] = 1;
++newBlacklisted;
}
}
if (whitelisted - newBlacklisted == 1)
{
// This node is dominated by the closest cluster.
counts[closestCluster] += referenceNode.NumDescendants();
newCentroids.col(closestCluster) += referenceNode.NumDescendants() *
referenceNode.Stat().Centroid();
return DBL_MAX;
}
// Perform the base case here.
for (size_t i = 0; i < referenceNode.NumPoints(); ++i)
{
size_t bestCluster = centroids.n_cols;
double bestDistance = DBL_MAX;
for (size_t c = 0; c < centroids.n_cols; ++c)
{
if (referenceNode.Stat().Blacklist()[c] == 1)
continue;
++distanceCalculations;
// The reference index is the index of the data point.
const double distance = metric.Evaluate(centroids.col(c),
dataset.col(referenceNode.Point(i)));
if (distance < bestDistance)
{
bestDistance = distance;
bestCluster = c;
}
}
// Add to resulting centroid.
newCentroids.col(bestCluster) += dataset.col(referenceNode.Point(i));
++counts(bestCluster);
}
// Otherwise, we're not sure, so we can't prune. Recursion order doesn't make
// a difference, so we'll just return a score of 0.
return 0.0;
}
void CheckTrees(TreeType& tree,
TreeType& xmlTree,
TreeType& textTree,
TreeType& binaryTree)
{
const typename TreeType::Mat* dataset = &tree.Dataset();
// Make sure that the data matrices are the same.
if (tree.Parent() == NULL)
{
CheckMatrices(*dataset,
xmlTree.Dataset(),
textTree.Dataset(),
binaryTree.Dataset());
// Also ensure that the other parents are null too.
BOOST_REQUIRE_EQUAL(xmlTree.Parent(), (TreeType*) NULL);
BOOST_REQUIRE_EQUAL(textTree.Parent(), (TreeType*) NULL);
BOOST_REQUIRE_EQUAL(binaryTree.Parent(), (TreeType*) NULL);
}
// Make sure the number of children is the same.
BOOST_REQUIRE_EQUAL(tree.NumChildren(), xmlTree.NumChildren());
BOOST_REQUIRE_EQUAL(tree.NumChildren(), textTree.NumChildren());
BOOST_REQUIRE_EQUAL(tree.NumChildren(), binaryTree.NumChildren());
// Make sure the number of descendants is the same.
BOOST_REQUIRE_EQUAL(tree.NumDescendants(), xmlTree.NumDescendants());
BOOST_REQUIRE_EQUAL(tree.NumDescendants(), textTree.NumDescendants());
BOOST_REQUIRE_EQUAL(tree.NumDescendants(), binaryTree.NumDescendants());
// Make sure the number of points is the same.
BOOST_REQUIRE_EQUAL(tree.NumPoints(), xmlTree.NumPoints());
BOOST_REQUIRE_EQUAL(tree.NumPoints(), textTree.NumPoints());
BOOST_REQUIRE_EQUAL(tree.NumPoints(), binaryTree.NumPoints());
// Check that each point is the same.
for (size_t i = 0; i < tree.NumPoints(); ++i)
{
BOOST_REQUIRE_EQUAL(tree.Point(i), xmlTree.Point(i));
BOOST_REQUIRE_EQUAL(tree.Point(i), textTree.Point(i));
BOOST_REQUIRE_EQUAL(tree.Point(i), binaryTree.Point(i));
}
// Check that the parent distance is the same.
BOOST_REQUIRE_CLOSE(tree.ParentDistance(), xmlTree.ParentDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.ParentDistance(), textTree.ParentDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.ParentDistance(), binaryTree.ParentDistance(), 1e-8);
// Check that the furthest descendant distance is the same.
BOOST_REQUIRE_CLOSE(tree.FurthestDescendantDistance(),
xmlTree.FurthestDescendantDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.FurthestDescendantDistance(),
textTree.FurthestDescendantDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.FurthestDescendantDistance(),
binaryTree.FurthestDescendantDistance(), 1e-8);
// Check that the minimum bound distance is the same.
BOOST_REQUIRE_CLOSE(tree.MinimumBoundDistance(),
xmlTree.MinimumBoundDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.MinimumBoundDistance(),
textTree.MinimumBoundDistance(), 1e-8);
BOOST_REQUIRE_CLOSE(tree.MinimumBoundDistance(),
binaryTree.MinimumBoundDistance(), 1e-8);
// Recurse into the children.
for (size_t i = 0; i < tree.NumChildren(); ++i)
{
// Check that the child dataset is the same.
BOOST_REQUIRE_EQUAL(&xmlTree.Dataset(), &xmlTree.Child(i).Dataset());
BOOST_REQUIRE_EQUAL(&textTree.Dataset(), &textTree.Child(i).Dataset());
BOOST_REQUIRE_EQUAL(&binaryTree.Dataset(), &binaryTree.Child(i).Dataset());
// Make sure the parent link is right.
BOOST_REQUIRE_EQUAL(xmlTree.Child(i).Parent(), &xmlTree);
BOOST_REQUIRE_EQUAL(textTree.Child(i).Parent(), &textTree);
BOOST_REQUIRE_EQUAL(binaryTree.Child(i).Parent(), &binaryTree);
CheckTrees(tree.Child(i), xmlTree.Child(i), textTree.Child(i),
binaryTree.Child(i));
}
}
inline double NeighborSearchRules<SortPolicy, MetricType, TreeType>::
CalculateBound(TreeType& queryNode) const
{
// We have five possible bounds, and we must take the best of them all. We
// don't use min/max here, but instead "best/worst", because this is general
// to the nearest-neighbors/furthest-neighbors cases. For nearest neighbors,
// min = best, max = worst.
//
// (1) worst ( worst_{all points p in queryNode} D_p[k],
// worst_{all children c in queryNode} B(c) );
// (2) best_{all points p in queryNode} D_p[k] + worst child distance +
// worst descendant distance;
// (3) best_{all children c in queryNode} B(c) +
// 2 ( worst descendant distance of queryNode -
// worst descendant distance of c );
// (4) B_1(parent of queryNode)
// (5) B_2(parent of queryNode);
//
// D_p[k] is the current k'th candidate distance for point p.
// So we will loop over the points in queryNode and the children in queryNode
// to calculate all five of these quantities.
// Hm, can we populate our distances vector with estimates from the parent?
// This is written specifically for the cover tree and assumes only one point
// in a node.
// if (queryNode.Parent() != NULL && queryNode.NumPoints() > 0)
// {
// size_t parentIndexStart = 0;
// for (size_t i = 0; i < neighbors.n_rows; ++i)
// {
// const double pointDistance = distances(i, queryNode.Point(0));
// if (pointDistance == DBL_MAX)
// {
// // Cool, can we take an estimate from the parent?
// const double parentWorstBound = distances(distances.n_rows - 1,
// queryNode.Parent()->Point(0));
// if (parentWorstBound != DBL_MAX)
// {
// const double parentAdjustedDistance = parentWorstBound +
// queryNode.ParentDistance();
// distances(i, queryNode.Point(0)) = parentAdjustedDistance;
// }
// }
// }
// }
double worstPointDistance = SortPolicy::BestDistance();
double bestPointDistance = SortPolicy::WorstDistance();
// Loop over all points in this node to find the best and worst distance
// candidates (for (1) and (2)).
for (size_t i = 0; i < queryNode.NumPoints(); ++i)
{
const double distance = distances(distances.n_rows - 1,
queryNode.Point(i));
if (SortPolicy::IsBetter(distance, bestPointDistance))
bestPointDistance = distance;
if (SortPolicy::IsBetter(worstPointDistance, distance))
worstPointDistance = distance;
}
// Loop over all the children in this node to find the worst bound (for (1))
// and the best bound with the correcting factor for descendant distances (for
// (3)).
double worstChildBound = SortPolicy::BestDistance();
double bestAdjustedChildBound = SortPolicy::WorstDistance();
const double queryMaxDescendantDistance =
queryNode.FurthestDescendantDistance();
for (size_t i = 0; i < queryNode.NumChildren(); ++i)
{
const double firstBound = queryNode.Child(i).Stat().FirstBound();
const double secondBound = queryNode.Child(i).Stat().SecondBound();
const double childMaxDescendantDistance =
queryNode.Child(i).FurthestDescendantDistance();
if (SortPolicy::IsBetter(worstChildBound, firstBound))
worstChildBound = firstBound;
// Now calculate adjustment for maximum descendant distances.
const double adjustedBound = SortPolicy::CombineWorst(secondBound,
2 * (queryMaxDescendantDistance - childMaxDescendantDistance));
if (SortPolicy::IsBetter(adjustedBound, bestAdjustedChildBound))
bestAdjustedChildBound = adjustedBound;
}
// This is bound (1).
const double firstBound =
(SortPolicy::IsBetter(worstPointDistance, worstChildBound)) ?
worstChildBound : worstPointDistance;
// This is bound (2).
const double secondBound = SortPolicy::CombineWorst(
SortPolicy::CombineWorst(bestPointDistance, queryMaxDescendantDistance),
queryNode.FurthestPointDistance());
// Bound (3) is bestAdjustedChildBound.
// Bounds (4) and (5) are the parent bounds.
const double fourthBound = (queryNode.Parent() != NULL) ?
queryNode.Parent()->Stat().FirstBound() : SortPolicy::WorstDistance();
// const double fifthBound = (queryNode.Parent() != NULL) ?
// queryNode.Parent()->Stat().SecondBound() -
// queryNode.Parent()->FurthestDescendantDistance() -
// queryNode.Parent()->FurthestPointDistance() + queryMaxDescendantDistance +
// queryNode.FurthestPointDistance() + queryNode.ParentDistance() :
// SortPolicy::WorstDistance();
// Now, we will take the best of these. Unfortunately due to the way
// IsBetter() is defined, this sort of has to be a little ugly.
// The variable interA represents the first bound (B_1), which is the worst
// candidate distance of any descendants of this node.
// The variable interC represents the second bound (B_2), which is a bound on
// the worst distance of any descendants of this node assembled using the best
// descendant candidate distance modified using the furthest descendant
// distance.
const double interA = (SortPolicy::IsBetter(firstBound, fourthBound)) ?
firstBound : fourthBound;
const double interB =
(SortPolicy::IsBetter(bestAdjustedChildBound, secondBound)) ?
bestAdjustedChildBound : secondBound;
// const double interC = (SortPolicy::IsBetter(interB, fifthBound)) ? interB :
// fifthBound;
// Update the first and second bounds of the node.
queryNode.Stat().FirstBound() = interA;
queryNode.Stat().SecondBound() = interB;
// Update the actual bound of the node.
queryNode.Stat().Bound() = (SortPolicy::IsBetter(interA, interB)) ? interB :
interB;
return queryNode.Stat().Bound();
}
double FastMKSRules<KernelType, TreeType>::CalculateBound(TreeType& queryNode)
const
{
// We have four possible bounds -- just like NeighborSearchRules, but they are
// slightly different in this context.
//
// (1) min ( min_{all points p in queryNode} P_p[k],
// min_{all children c in queryNode} B(c) );
// (2) max_{all points p in queryNode} P_p[k] + (worst child distance + worst
// descendant distance) sqrt(K(I_p[k], I_p[k]));
// (3) max_{all children c in queryNode} B(c) + <-- not done yet. ignored.
// (4) B(parent of queryNode);
double worstPointKernel = DBL_MAX;
double bestAdjustedPointKernel = -DBL_MAX;
const double queryDescendantDistance = queryNode.FurthestDescendantDistance();
// Loop over all points in this node to find the best and worst.
for (size_t i = 0; i < queryNode.NumPoints(); ++i)
{
const size_t point = queryNode.Point(i);
if (products(products.n_rows - 1, point) < worstPointKernel)
worstPointKernel = products(products.n_rows - 1, point);
if (products(products.n_rows - 1, point) == -DBL_MAX)
continue; // Avoid underflow.
// This should be (queryDescendantDistance + centroidDistance) for any tree
// but it works for cover trees since centroidDistance = 0 for cover trees.
const double candidateKernel = products(products.n_rows - 1, point) -
queryDescendantDistance *
referenceKernels[indices(indices.n_rows - 1, point)];
if (candidateKernel > bestAdjustedPointKernel)
bestAdjustedPointKernel = candidateKernel;
}
// Loop over all the children in the node.
double worstChildKernel = DBL_MAX;
for (size_t i = 0; i < queryNode.NumChildren(); ++i)
{
if (queryNode.Child(i).Stat().Bound() < worstChildKernel)
worstChildKernel = queryNode.Child(i).Stat().Bound();
}
// Now assemble bound (1).
const double firstBound = (worstPointKernel < worstChildKernel) ?
worstPointKernel : worstChildKernel;
// Bound (2) is bestAdjustedPointKernel.
const double fourthBound = (queryNode.Parent() == NULL) ? -DBL_MAX :
queryNode.Parent()->Stat().Bound();
// Pick the best of these bounds.
const double interA = (firstBound > bestAdjustedPointKernel) ? firstBound :
bestAdjustedPointKernel;
// const double interA = 0.0;
const double interB = fourthBound;
return (interA > interB) ? interA : interB;
}