static int GetSplitPolicy(const TreeType& child,
const size_t axis,
const typename TreeType::ElemType cut)
{
if (child.Bound()[axis].Hi() <= cut)
return AssignToFirstTree;
else if (child.Bound()[axis].Lo() >= cut)
return AssignToSecondTree;
return SplitRequired;
}
void CheckSplit(const TreeType& tree)
{
typedef typename TreeType::ElemType ElemType;
typedef typename std::conditional<sizeof(ElemType) * CHAR_BIT <= 32,
uint32_t,
uint64_t>::type AddressElemType;
if (tree.IsLeaf())
return;
arma::Col<AddressElemType> lo(tree.Bound().Dim());
arma::Col<AddressElemType> hi(tree.Bound().Dim());
lo.fill(std::numeric_limits<AddressElemType>::max());
hi.fill(0);
arma::Col<AddressElemType> address(tree.Bound().Dim());
// Find the highest address of the left node.
for (size_t i = 0; i < tree.Left()->NumDescendants(); i++)
{
addr::PointToAddress(address,
tree.Dataset().col(tree.Left()->Descendant(i)));
if (addr::CompareAddresses(address, hi) > 0)
hi = address;
}
// Find the lowest address of the right node.
for (size_t i = 0; i < tree.Right()->NumDescendants(); i++)
{
addr::PointToAddress(address,
tree.Dataset().col(tree.Right()->Descendant(i)));
if (addr::CompareAddresses(address, lo) < 0)
lo = address;
}
// Addresses in the left node should be less than addresses in the right node.
BOOST_REQUIRE_LE(addr::CompareAddresses(hi, lo), 0);
CheckSplit(*tree.Left());
CheckSplit(*tree.Right());
}
void CheckContainment(const TreeType& tree)
{
if (tree.NumChildren() == 0)
{
for (size_t i = 0; i < tree.Count(); i++)
BOOST_REQUIRE(tree.Bound().Contains(
tree.Dataset().unsafe_col(tree.Points()[i])));
}
else
{
for (size_t i = 0; i < tree.NumChildren(); i++)
{
for (size_t j = 0; j < tree.Bound().Dim(); j++)
BOOST_REQUIRE(tree.Bound()[j].Contains(tree.Children()[i]->Bound()[j]));
CheckContainment(*(tree.Children()[i]));
}
}
}
void CheckExactContainment(const TreeType& tree)
{
if (tree.NumChildren() == 0)
{
for (size_t i = 0; i < tree.Bound().Dim(); i++)
{
double min = DBL_MAX;
double max = -1.0 * DBL_MAX;
for(size_t j = 0; j < tree.Count(); j++)
{
if (tree.LocalDataset().col(j)[i] < min)
min = tree.LocalDataset().col(j)[i];
if (tree.LocalDataset().col(j)[i] > max)
max = tree.LocalDataset().col(j)[i];
}
BOOST_REQUIRE_EQUAL(max, tree.Bound()[i].Hi());
BOOST_REQUIRE_EQUAL(min, tree.Bound()[i].Lo());
}
}
else
{
for (size_t i = 0; i < tree.Bound().Dim(); i++)
{
double min = DBL_MAX;
double max = -1.0 * DBL_MAX;
for (size_t j = 0; j < tree.NumChildren(); j++)
{
if(tree.Child(j).Bound()[i].Lo() < min)
min = tree.Child(j).Bound()[i].Lo();
if(tree.Child(j).Bound()[i].Hi() > max)
max = tree.Child(j).Bound()[i].Hi();
}
BOOST_REQUIRE_EQUAL(max, tree.Bound()[i].Hi());
BOOST_REQUIRE_EQUAL(min, tree.Bound()[i].Lo());
}
for (size_t i = 0; i < tree.NumChildren(); i++)
CheckExactContainment(tree.Child(i));
}
}
void CheckBound(const TreeType& tree)
{
typedef typename TreeType::ElemType ElemType;
for (size_t i = 0; i < tree.NumDescendants(); i++)
{
arma::Col<ElemType> point = tree.Dataset().col(tree.Descendant(i));
// Check that the point is contained in the bound.
BOOST_REQUIRE_EQUAL(true, tree.Bound().Contains(point));
const arma::Mat<ElemType>& loBound = tree.Bound().LoBound();
const arma::Mat<ElemType>& hiBound = tree.Bound().HiBound();
// Ensure that there is a hyperrectangle that contains the point.
bool success = false;
for (size_t j = 0; j < tree.Bound().NumBounds(); j++)
{
success = true;
for (size_t k = 0; k < loBound.n_rows; k++)
{
if (point[k] < loBound(k, j) - 1e-14 * std::fabs(loBound(k, j)) ||
point[k] > hiBound(k, j) + 1e-14 * std::fabs(hiBound(k, j)))
{
success = false;
break;
}
}
if (success)
break;
}
BOOST_REQUIRE_EQUAL(success, true);
}
if (!tree.IsLeaf())
{
CheckBound(*tree.Left());
CheckBound(*tree.Right());
}
}
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 CheckDistance(TreeType& tree, TreeType* node = NULL)
{
typedef typename TreeType::ElemType ElemType;
if (node == NULL)
{
node = &tree;
while (node->Parent() != NULL)
node = node->Parent();
CheckDistance<TreeType, MetricType>(tree, node);
for (size_t j = 0; j < tree.Dataset().n_cols; j++)
{
const arma::Col<ElemType>& point = tree. Dataset().col(j);
ElemType maxDist = 0;
ElemType minDist = std::numeric_limits<ElemType>::max();
for (size_t i = 0; i < tree.NumDescendants(); i++)
{
ElemType dist = MetricType::Evaluate(
tree.Dataset().col(tree.Descendant(i)),
tree.Dataset().col(j));
if (dist > maxDist)
maxDist = dist;
if (dist < minDist)
minDist = dist;
}
BOOST_REQUIRE_LE(tree.Bound().MinDistance(point), minDist *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
BOOST_REQUIRE_LE(maxDist, tree.Bound().MaxDistance(point) *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
math::RangeType<ElemType> r = tree.Bound().RangeDistance(point);
BOOST_REQUIRE_LE(r.Lo(), minDist *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
BOOST_REQUIRE_LE(maxDist, r.Hi() *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
}
if (!tree.IsLeaf())
{
CheckDistance<TreeType, MetricType>(*tree.Left());
CheckDistance<TreeType, MetricType>(*tree.Right());
}
}
else
{
if (&tree != node)
{
ElemType maxDist = 0;
ElemType minDist = std::numeric_limits<ElemType>::max();
for (size_t i = 0; i < tree.NumDescendants(); i++)
for (size_t j = 0; j < node->NumDescendants(); j++)
{
ElemType dist = MetricType::Evaluate(
tree.Dataset().col(tree.Descendant(i)),
node->Dataset().col(node->Descendant(j)));
if (dist > maxDist)
maxDist = dist;
if (dist < minDist)
minDist = dist;
}
BOOST_REQUIRE_LE(tree.Bound().MinDistance(node->Bound()), minDist *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
BOOST_REQUIRE_LE(maxDist, tree.Bound().MaxDistance(node->Bound()) *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
math::RangeType<ElemType> r = tree.Bound().RangeDistance(node->Bound());
BOOST_REQUIRE_LE(r.Lo(), minDist *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
BOOST_REQUIRE_LE(maxDist, r.Hi() *
(1.0 + 10 * std::numeric_limits<ElemType>::epsilon()));
}
if (!node->IsLeaf())
{
CheckDistance<TreeType, MetricType>(tree, node->Left());
CheckDistance<TreeType, MetricType>(tree, node->Right());
}
}
}
