double RangeSearchRules<MetricType, TreeType>::Score(const size_t queryIndex,
TreeType& referenceNode)
{
// We must get the minimum and maximum distances and store them in this
// object.
math::Range distances;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// In this situation, we calculate the base case. So we should check to be
// sure we haven't already done that.
double baseCase;
if (tree::TreeTraits<TreeType>::HasSelfChildren &&
(referenceNode.Parent() != NULL) &&
(referenceNode.Point(0) == referenceNode.Parent()->Point(0)))
{
// If the tree has self-children and this is a self-child, the base case
// was already calculated.
baseCase = referenceNode.Parent()->Stat().LastDistance();
lastQueryIndex = queryIndex;
lastReferenceIndex = referenceNode.Point(0);
}
else
{
// We must calculate the base case by hand.
baseCase = BaseCase(queryIndex, referenceNode.Point(0));
}
// This may be possibly loose for non-ball bound trees.
distances.Lo() = baseCase - referenceNode.FurthestDescendantDistance();
distances.Hi() = baseCase + referenceNode.FurthestDescendantDistance();
// Update last distance calculation.
referenceNode.Stat().LastDistance() = baseCase;
}
else
{
distances = referenceNode.RangeDistance(querySet.unsafe_col(queryIndex));
}
// If the ranges do not overlap, prune this node.
if (!distances.Contains(range))
return DBL_MAX;
// In this case, all of the points in the reference node will be part of the
// results.
if ((distances.Lo() >= range.Lo()) && (distances.Hi() <= range.Hi()))
{
AddResult(queryIndex, referenceNode);
return DBL_MAX; // We don't need to go any deeper.
}
// Otherwise the score doesn't matter. Recursion order is irrelevant in
// range search.
return 0.0;
}
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();
}
inline double NeighborSearchRules<SortPolicy, MetricType, TreeType>::Score(
const size_t queryIndex,
TreeType& referenceNode)
{
++scores; // Count number of Score() calls.
double distance;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// The first point in the tree is the centroid. So we can then calculate
// the base case between that and the query point.
double baseCase = -1.0;
if (tree::TreeTraits<TreeType>::HasSelfChildren)
{
// If the parent node is the same, then we have already calculated the
// base case.
if ((referenceNode.Parent() != NULL) &&
(referenceNode.Point(0) == referenceNode.Parent()->Point(0)))
baseCase = referenceNode.Parent()->Stat().LastDistance();
else
baseCase = BaseCase(queryIndex, referenceNode.Point(0));
// Save this evaluation.
referenceNode.Stat().LastDistance() = baseCase;
}
distance = SortPolicy::CombineBest(baseCase,
referenceNode.FurthestDescendantDistance());
}
else
{
distance = SortPolicy::BestPointToNodeDistance(querySet.col(queryIndex),
&referenceNode);
}
// Compare against the best k'th distance for this query point so far.
const double bestDistance = distances(distances.n_rows - 1, queryIndex);
return (SortPolicy::IsBetter(distance, bestDistance)) ? distance : DBL_MAX;
}
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();
}
inline double NeighborSearchRules<SortPolicy, MetricType, TreeType>::Score(
TreeType& queryNode,
TreeType& referenceNode)
{
++scores; // Count number of Score() calls.
// Update our bound.
const double bestDistance = CalculateBound(queryNode);
// Use the traversal info to see if a parent-child or parent-parent prune is
// possible. This is a looser bound than we could make, but it might be
// sufficient.
const double queryParentDist = queryNode.ParentDistance();
const double queryDescDist = queryNode.FurthestDescendantDistance();
const double refParentDist = referenceNode.ParentDistance();
const double refDescDist = referenceNode.FurthestDescendantDistance();
const double score = traversalInfo.LastScore();
double adjustedScore;
// We want to set adjustedScore to be the distance between the centroid of the
// last query node and last reference node. We will do this by adjusting the
// last score. In some cases, we can just use the last base case.
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
adjustedScore = traversalInfo.LastBaseCase();
}
else if (score == 0.0) // Nothing we can do here.
{
adjustedScore = 0.0;
}
else
{
// The last score is equal to the distance between the centroids minus the
// radii of the query and reference bounds along the axis of the line
// between the two centroids. In the best case, these radii are the
// furthest descendant distances, but that is not always true. It would
// take too long to calculate the exact radii, so we are forced to use
// MinimumBoundDistance() as a lower-bound approximation.
const double lastQueryDescDist =
traversalInfo.LastQueryNode()->MinimumBoundDistance();
const double lastRefDescDist =
traversalInfo.LastReferenceNode()->MinimumBoundDistance();
adjustedScore = SortPolicy::CombineWorst(score, lastQueryDescDist);
adjustedScore = SortPolicy::CombineWorst(score, lastRefDescDist);
}
// Assemble an adjusted score. For nearest neighbor search, this adjusted
// score is a lower bound on MinDistance(queryNode, referenceNode) that is
// assembled without actually calculating MinDistance(). For furthest
// neighbor search, it is an upper bound on
// MaxDistance(queryNode, referenceNode). If the traversalInfo isn't usable
// then the node should not be pruned by this.
if (traversalInfo.LastQueryNode() == queryNode.Parent())
{
const double queryAdjust = queryParentDist + queryDescDist;
adjustedScore = SortPolicy::CombineBest(adjustedScore, queryAdjust);
}
else if (traversalInfo.LastQueryNode() == &queryNode)
{
adjustedScore = SortPolicy::CombineBest(adjustedScore, queryDescDist);
}
else
{
// The last query node wasn't this query node or its parent. So we force
// the adjustedScore to be such that this combination can't be pruned here,
// because we don't really know anything about it.
// It would be possible to modify this section to try and make a prune based
// on the query descendant distance and the distance between the query node
// and last traversal query node, but this case doesn't actually happen for
// kd-trees or cover trees.
adjustedScore = SortPolicy::BestDistance();
}
if (traversalInfo.LastReferenceNode() == referenceNode.Parent())
{
const double refAdjust = refParentDist + refDescDist;
adjustedScore = SortPolicy::CombineBest(adjustedScore, refAdjust);
}
else if (traversalInfo.LastReferenceNode() == &referenceNode)
{
adjustedScore = SortPolicy::CombineBest(adjustedScore, refDescDist);
}
else
{
// The last reference node wasn't this reference node or its parent. So we
// force the adjustedScore to be such that this combination can't be pruned
// here, because we don't really know anything about it.
// It would be possible to modify this section to try and make a prune based
// on the reference descendant distance and the distance between the
// reference node and last traversal reference node, but this case doesn't
// actually happen for kd-trees or cover trees.
adjustedScore = SortPolicy::BestDistance();
}
// Can we prune?
if (SortPolicy::IsBetter(bestDistance, adjustedScore))
{
if (!(tree::TreeTraits<TreeType>::FirstPointIsCentroid && score == 0.0))
{
// There isn't any need to set the traversal information because no
// descendant combinations will be visited, and those are the only
// combinations that would depend on the traversal information.
return DBL_MAX;
}
}
double distance;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// The first point in the node is the centroid, so we can calculate the
// distance between the two points using BaseCase() and then find the
// bounds. This is potentially loose for non-ball bounds.
double baseCase = -1.0;
if (tree::TreeTraits<TreeType>::HasSelfChildren &&
(traversalInfo.LastQueryNode()->Point(0) == queryNode.Point(0)) &&
(traversalInfo.LastReferenceNode()->Point(0) == referenceNode.Point(0)))
{
// We already calculated it.
baseCase = traversalInfo.LastBaseCase();
}
else
{
baseCase = BaseCase(queryNode.Point(0), referenceNode.Point(0));
}
distance = SortPolicy::CombineBest(baseCase,
queryNode.FurthestDescendantDistance() +
referenceNode.FurthestDescendantDistance());
lastQueryIndex = queryNode.Point(0);
lastReferenceIndex = referenceNode.Point(0);
lastBaseCase = baseCase;
traversalInfo.LastBaseCase() = baseCase;
}
else
{
distance = SortPolicy::BestNodeToNodeDistance(&queryNode, &referenceNode);
}
if (SortPolicy::IsBetter(distance, bestDistance))
{
// Set traversal information.
traversalInfo.LastQueryNode() = &queryNode;
traversalInfo.LastReferenceNode() = &referenceNode;
traversalInfo.LastScore() = distance;
return distance;
}
else
{
// There isn't any need to set the traversal information because no
// descendant combinations will be visited, and those are the only
// combinations that would depend on the traversal information.
return DBL_MAX;
}
}
double RangeSearchRules<MetricType, TreeType>::Score(TreeType& queryNode,
TreeType& referenceNode)
{
math::Range distances;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// It is possible that the base case has already been calculated.
double baseCase = 0.0;
bool alreadyDone = false;
if (tree::TreeTraits<TreeType>::HasSelfChildren)
{
TreeType* lastQuery = (TreeType*) referenceNode.Stat().LastDistanceNode();
TreeType* lastRef = (TreeType*) queryNode.Stat().LastDistanceNode();
// Did the query node's last combination do the base case?
if ((lastRef != NULL) && (referenceNode.Point(0) == lastRef->Point(0)))
{
baseCase = queryNode.Stat().LastDistance();
alreadyDone = true;
}
// Did the reference node's last combination do the base case?
if ((lastQuery != NULL) && (queryNode.Point(0) == lastQuery->Point(0)))
{
baseCase = referenceNode.Stat().LastDistance();
alreadyDone = true;
}
// If the query node is a self-child, did the query parent's last
// combination do the base case?
if ((queryNode.Parent() != NULL) &&
(queryNode.Point(0) == queryNode.Parent()->Point(0)))
{
TreeType* lastParentRef = (TreeType*)
queryNode.Parent()->Stat().LastDistanceNode();
if ((lastParentRef != NULL) &&
(referenceNode.Point(0) == lastParentRef->Point(0)))
{
baseCase = queryNode.Parent()->Stat().LastDistance();
alreadyDone = true;
}
}
// If the reference node is a self-child, did the reference parent's last
// combination do the base case?
if ((referenceNode.Parent() != NULL) &&
(referenceNode.Point(0) == referenceNode.Parent()->Point(0)))
{
TreeType* lastQueryRef = (TreeType*)
referenceNode.Parent()->Stat().LastDistanceNode();
if ((lastQueryRef != NULL) &&
(queryNode.Point(0) == lastQueryRef->Point(0)))
{
baseCase = referenceNode.Parent()->Stat().LastDistance();
alreadyDone = true;
}
}
}
if (!alreadyDone)
{
// We must calculate the base case.
baseCase = BaseCase(queryNode.Point(0), referenceNode.Point(0));
}
else
{
// Make sure that if BaseCase() is called, we don't duplicate results.
lastQueryIndex = queryNode.Point(0);
lastReferenceIndex = referenceNode.Point(0);
}
distances.Lo() = baseCase - queryNode.FurthestDescendantDistance()
- referenceNode.FurthestDescendantDistance();
distances.Hi() = baseCase + queryNode.FurthestDescendantDistance()
+ referenceNode.FurthestDescendantDistance();
// Update the last distances performed for the query and reference node.
queryNode.Stat().LastDistanceNode() = (void*) &referenceNode;
queryNode.Stat().LastDistance() = baseCase;
referenceNode.Stat().LastDistanceNode() = (void*) &queryNode;
referenceNode.Stat().LastDistance() = baseCase;
}
else
{
// Just perform the calculation.
distances = referenceNode.RangeDistance(&queryNode);
}
// If the ranges do not overlap, prune this node.
if (!distances.Contains(range))
return DBL_MAX;
// In this case, all of the points in the reference node will be part of all
// the results for each point in the query node.
if ((distances.Lo() >= range.Lo()) && (distances.Hi() <= range.Hi()))
{
for (size_t i = 0; i < queryNode.NumDescendants(); ++i)
AddResult(queryNode.Descendant(i), referenceNode);
return DBL_MAX; // We don't need to go any deeper.
}
// Otherwise the score doesn't matter. Recursion order is irrelevant in range
// search.
return 0.0;
}
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;
}
double FastMKSRules<KernelType, TreeType>::Score(TreeType& queryNode,
TreeType& referenceNode)
{
// Update and get the query node's bound.
queryNode.Stat().Bound() = CalculateBound(queryNode);
const double bestKernel = queryNode.Stat().Bound();
// First, see if we can make a parent-child or parent-parent prune. These
// four bounds on the maximum kernel value are looser than the bound normally
// used, but they can prevent a base case from needing to be calculated.
// Convenience caching so lines are shorter.
const double queryParentDist = queryNode.ParentDistance();
const double queryDescDist = queryNode.FurthestDescendantDistance();
const double refParentDist = referenceNode.ParentDistance();
const double refDescDist = referenceNode.FurthestDescendantDistance();
double adjustedScore = traversalInfo.LastBaseCase();
const double queryDistBound = (queryParentDist + queryDescDist);
const double refDistBound = (refParentDist + refDescDist);
double dualQueryTerm;
double dualRefTerm;
// The parent-child and parent-parent prunes work by applying the same pruning
// condition as when the parent node was used, except they are tighter because
// queryDistBound < queryNode.Parent()->FurthestDescendantDistance()
// and
// refDistBound < referenceNode.Parent()->FurthestDescendantDistance()
// so we construct the same bounds that were used when Score() was called with
// the parents, except with the tighter distance bounds. Sometimes this
// allows us to prune nodes without evaluating the base cases between them.
if (traversalInfo.LastQueryNode() == queryNode.Parent())
{
// We can assume that queryNode.Parent() != NULL, because at the root node
// combination, the traversalInfo.LastQueryNode() pointer will _not_ be
// NULL. We also should be guaranteed that
// traversalInfo.LastReferenceNode() is either the reference node or the
// parent of the reference node.
adjustedScore += queryDistBound *
traversalInfo.LastReferenceNode()->Stat().SelfKernel();
dualQueryTerm = queryDistBound;
}
else
{
// The query parent could be NULL, which does weird things and we have to
// consider.
if (traversalInfo.LastReferenceNode() != NULL)
{
adjustedScore += queryDescDist *
traversalInfo.LastReferenceNode()->Stat().SelfKernel();
dualQueryTerm = queryDescDist;
}
else
{
// This makes it so a child-parent (or parent-parent) prune is not
// possible.
dualQueryTerm = 0.0;
adjustedScore = bestKernel;
}
}
if (traversalInfo.LastReferenceNode() == referenceNode.Parent())
{
// We can assume that referenceNode.Parent() != NULL, because at the root
// node combination, the traversalInfo.LastReferenceNode() pointer will
// _not_ be NULL.
adjustedScore += refDistBound *
traversalInfo.LastQueryNode()->Stat().SelfKernel();
dualRefTerm = refDistBound;
}
else
{
// The reference parent could be NULL, which does weird things and we have
// to consider.
if (traversalInfo.LastQueryNode() != NULL)
{
adjustedScore += refDescDist *
traversalInfo.LastQueryNode()->Stat().SelfKernel();
dualRefTerm = refDescDist;
}
else
{
// This makes it so a child-parent (or parent-parent) prune is not
// possible.
dualRefTerm = 0.0;
adjustedScore = bestKernel;
}
}
// Now add the dual term.
adjustedScore += (dualQueryTerm * dualRefTerm);
if (adjustedScore < bestKernel)
{
// It is not possible that this node combination can contain a point
// combination with kernel value better than the minimum kernel value to
// improve any of the results, so we can prune it.
return DBL_MAX;
}
// We were unable to perform a parent-child or parent-parent prune, so now we
// must calculate kernel evaluation, if necessary.
double kernelEval = 0.0;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// For this type of tree, we may have already calculated the base case in
// the parents.
if ((traversalInfo.LastQueryNode() != NULL) &&
(traversalInfo.LastReferenceNode() != NULL) &&
(traversalInfo.LastQueryNode()->Point(0) == queryNode.Point(0)) &&
(traversalInfo.LastReferenceNode()->Point(0) == referenceNode.Point(0)))
{
// Base case already done.
kernelEval = traversalInfo.LastBaseCase();
// When BaseCase() is called after Score(), these must be correct so that
// another kernel evaluation is not performed.
lastQueryIndex = queryNode.Point(0);
lastReferenceIndex = referenceNode.Point(0);
}
else
{
// The kernel must be evaluated, but it is between points in the dataset,
// so we can call BaseCase(). BaseCase() will set lastQueryIndex and
// lastReferenceIndex correctly.
kernelEval = BaseCase(queryNode.Point(0), referenceNode.Point(0));
}
traversalInfo.LastBaseCase() = kernelEval;
}
else
{
// Calculate the maximum possible kernel value.
arma::vec queryCentroid;
arma::vec refCentroid;
queryNode.Centroid(queryCentroid);
referenceNode.Centroid(refCentroid);
kernelEval = kernel.Evaluate(queryCentroid, refCentroid);
traversalInfo.LastBaseCase() = kernelEval;
}
++scores;
double maxKernel;
if (kernel::KernelTraits<KernelType>::IsNormalized)
{
// We have a tighter bound for normalized kernels.
const double querySqDist = std::pow(queryDescDist, 2.0);
const double refSqDist = std::pow(refDescDist, 2.0);
const double bothSqDist = std::pow((queryDescDist + refDescDist), 2.0);
if (kernelEval <= (1 - 0.5 * bothSqDist))
{
const double queryDelta = (1 - 0.5 * querySqDist);
const double queryGamma = queryDescDist * sqrt(1 - 0.25 * querySqDist);
const double refDelta = (1 - 0.5 * refSqDist);
const double refGamma = refDescDist * sqrt(1 - 0.25 * refSqDist);
maxKernel = kernelEval * (queryDelta * refDelta - queryGamma * refGamma) +
sqrt(1 - std::pow(kernelEval, 2.0)) *
(queryGamma * refDelta + queryDelta * refGamma);
}
else
{
maxKernel = 1.0;
}
}
else
{
// Use standard bound; kernel is not normalized.
const double refKernelTerm = queryDescDist *
referenceNode.Stat().SelfKernel();
const double queryKernelTerm = refDescDist * queryNode.Stat().SelfKernel();
maxKernel = kernelEval + refKernelTerm + queryKernelTerm +
(queryDescDist * refDescDist);
}
// Store relevant information for parent-child pruning.
traversalInfo.LastQueryNode() = &queryNode;
traversalInfo.LastReferenceNode() = &referenceNode;
// We return the inverse of the maximum kernel so that larger kernels are
// recursed into first.
return (maxKernel > bestKernel) ? (1.0 / maxKernel) : DBL_MAX;
}
double FastMKSRules<KernelType, TreeType>::Score(const size_t queryIndex,
TreeType& referenceNode)
{
// Compare with the current best.
const double bestKernel = products(products.n_rows - 1, queryIndex);
// See if we can perform a parent-child prune.
const double furthestDist = referenceNode.FurthestDescendantDistance();
if (referenceNode.Parent() != NULL)
{
double maxKernelBound;
const double parentDist = referenceNode.ParentDistance();
const double combinedDistBound = parentDist + furthestDist;
const double lastKernel = referenceNode.Parent()->Stat().LastKernel();
if (kernel::KernelTraits<KernelType>::IsNormalized)
{
const double squaredDist = std::pow(combinedDistBound, 2.0);
const double delta = (1 - 0.5 * squaredDist);
if (lastKernel <= delta)
{
const double gamma = combinedDistBound * sqrt(1 - 0.25 * squaredDist);
maxKernelBound = lastKernel * delta +
gamma * sqrt(1 - std::pow(lastKernel, 2.0));
}
else
{
maxKernelBound = 1.0;
}
}
else
{
maxKernelBound = lastKernel +
combinedDistBound * queryKernels[queryIndex];
}
if (maxKernelBound < bestKernel)
return DBL_MAX;
}
// Calculate the maximum possible kernel value, either by calculating the
// centroid or, if the centroid is a point, use that.
++scores;
double kernelEval;
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
// Could it be that this kernel evaluation has already been calculated?
if (tree::TreeTraits<TreeType>::HasSelfChildren &&
referenceNode.Parent() != NULL &&
referenceNode.Point(0) == referenceNode.Parent()->Point(0))
{
kernelEval = referenceNode.Parent()->Stat().LastKernel();
}
else
{
kernelEval = BaseCase(queryIndex, referenceNode.Point(0));
}
}
else
{
const arma::vec queryPoint = querySet.unsafe_col(queryIndex);
arma::vec refCentroid;
referenceNode.Centroid(refCentroid);
kernelEval = kernel.Evaluate(queryPoint, refCentroid);
}
referenceNode.Stat().LastKernel() = kernelEval;
double maxKernel;
if (kernel::KernelTraits<KernelType>::IsNormalized)
{
const double squaredDist = std::pow(furthestDist, 2.0);
const double delta = (1 - 0.5 * squaredDist);
if (kernelEval <= delta)
{
const double gamma = furthestDist * sqrt(1 - 0.25 * squaredDist);
maxKernel = kernelEval * delta +
gamma * sqrt(1 - std::pow(kernelEval, 2.0));
}
else
{
maxKernel = 1.0;
}
}
else
{
maxKernel = kernelEval + furthestDist * queryKernels[queryIndex];
}
// We return the inverse of the maximum kernel so that larger kernels are
// recursed into first.
return (maxKernel > bestKernel) ? (1.0 / maxKernel) : DBL_MAX;
}
