Trees and tree-building procedures. More...

Namespaces
	split

Classes
class	AllCategoricalSplit
	The AllCategoricalSplit is a splitting function that will split categorical features into many children: one child for each category. More...

class	AxisParallelProjVector
	AxisParallelProjVector defines an axis-parallel projection vector. More...

class	BestBinaryNumericSplit
	The BestBinaryNumericSplit is a splitting function for decision trees that will exhaustively search a numeric dimension for the best binary split. More...

class	BinaryNumericSplit
	The BinaryNumericSplit class implements the numeric feature splitting strategy devised by Gama, Rocha, and Medas in the following paper: More...

class	BinaryNumericSplitInfo

class	BinarySpaceTree
	A binary space partitioning tree, such as a KD-tree or a ball tree. More...

class	CategoricalSplitInfo

class	CompareCosineNode

class	CosineTree

class	CoverTree
	A cover tree is a tree specifically designed to speed up nearest-neighbor computation in high-dimensional spaces. More...

class	DecisionTree
	This class implements a generic decision tree learner. More...

class	DiscreteHilbertValue
	The DiscreteHilbertValue class stores Hilbert values for all of the points in a RectangleTree node, and calculates Hilbert values for new points. More...

class	EmptyStatistic
	Empty statistic if you are not interested in storing statistics in your tree. More...

class	ExampleTree
	This is not an actual space tree but instead an example tree that exists to show and document all the functions that mlpack trees must implement. More...

class	FirstPointIsRoot
	This class is meant to be used as a choice for the policy class RootPointPolicy of the CoverTree class. More...

class	GiniGain
	The Gini gain, a measure of set purity usable as a fitness function (FitnessFunction) for decision trees. More...

class	GiniImpurity

class	GreedySingleTreeTraverser

class	HilbertRTreeAuxiliaryInformation

class	HilbertRTreeDescentHeuristic
	This class chooses the best child of a node in a Hilbert R tree when inserting a new point. More...

class	HilbertRTreeSplit
	The splitting procedure for the Hilbert R tree. More...

class	HoeffdingCategoricalSplit
	This is the standard Hoeffding-bound categorical feature proposed in the paper below: More...

class	HoeffdingNumericSplit
	The HoeffdingNumericSplit class implements the numeric feature splitting strategy alluded to by Domingos and Hulten in the following paper: More...

class	HoeffdingTree
	The HoeffdingTree object represents all of the necessary information for a Hoeffding-bound-based decision tree. More...

class	HoeffdingTreeModel
	This class is a serializable Hoeffding tree model that can hold four different types of Hoeffding trees. More...

class	HyperplaneBase
	HyperplaneBase defines a splitting hyperplane based on a projection vector and projection value. More...

class	InformationGain
	The standard information gain criterion, used for calculating gain in decision trees. More...

struct	IsSpillTree

struct	IsSpillTree< tree::SpillTree< MetricType, StatisticType, MatType, HyperplaneType, SplitType > >

class	MeanSpaceSplit

class	MeanSplit
	A binary space partitioning tree node is split into its left and right child. More...

class	MidpointSpaceSplit

class	MidpointSplit
	A binary space partitioning tree node is split into its left and right child. More...

class	MinimalCoverageSweep
	The MinimalCoverageSweep class finds a partition along which we can split a node according to the coverage of two resulting nodes. More...

class	MinimalSplitsNumberSweep
	The MinimalSplitsNumberSweep class finds a partition along which we can split a node according to the number of required splits of the node. More...

class	NoAuxiliaryInformation

class	NumericSplitInfo

class	Octree

class	ProjVector
	ProjVector defines a general projection vector (not necessarily axis-parallel). More...

struct	QueueFrame

class	RectangleTree
	A rectangle type tree tree, such as an R-tree or X-tree. More...

class	RPlusPlusTreeAuxiliaryInformation

class	RPlusPlusTreeDescentHeuristic

class	RPlusPlusTreeSplitPolicy
	The RPlusPlusTreeSplitPolicy helps to determine the subtree into which we should insert a child of an intermediate node that is being split. More...

class	RPlusTreeDescentHeuristic

class	RPlusTreeSplit
	The RPlusTreeSplit class performs the split process of a node on overflow. More...

class	RPlusTreeSplitPolicy
	The RPlusPlusTreeSplitPolicy helps to determine the subtree into which we should insert a child of an intermediate node that is being split. More...

class	RPTreeMaxSplit
	This class splits a node by a random hyperplane. More...

class	RPTreeMeanSplit
	This class splits a binary space tree. More...

class	RStarTreeDescentHeuristic
	When descending a RectangleTree to insert a point, we need to have a way to choose a child node when the point isn't enclosed by any of them. More...

class	RStarTreeSplit
	A Rectangle Tree has new points inserted at the bottom. More...

class	RTreeDescentHeuristic
	When descending a RectangleTree to insert a point, we need to have a way to choose a child node when the point isn't enclosed by any of them. More...

class	RTreeSplit
	A Rectangle Tree has new points inserted at the bottom. More...

class	SpaceSplit

class	SpillTree
	A hybrid spill tree is a variant of binary space trees in which the children of a node can "spill over" each other, and contain shared datapoints. More...

class	TraversalInfo
	The TraversalInfo class holds traversal information which is used in dual-tree (and single-tree) traversals. More...

class	TreeTraits
	The TreeTraits class provides compile-time information on the characteristics of a given tree type. More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, bound::BallBound, SplitType > >
	This is a specialization of the TreeType class to the BallTree tree type. More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, bound::CellBound, SplitType > >
	This is a specialization of the TreeType class to the UBTree tree type. More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, bound::HollowBallBound, SplitType > >
	This is a specialization of the TreeType class to an arbitrary tree with HollowBallBound (currently only the vantage point tree is supported). More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, BoundType, RPTreeMaxSplit > >
	This is a specialization of the TreeType class to the max-split random projection tree. More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, BoundType, RPTreeMeanSplit > >
	This is a specialization of the TreeType class to the mean-split random projection tree. More...

class	TreeTraits< BinarySpaceTree< MetricType, StatisticType, MatType, BoundType, SplitType > >
	This is a specialization of the TreeTraits class to the BinarySpaceTree tree type. More...

class	TreeTraits< CoverTree< MetricType, StatisticType, MatType, RootPointPolicy > >
	The specialization of the TreeTraits class for the CoverTree tree type. More...

class	TreeTraits< Octree< MetricType, StatisticType, MatType > >
	This is a specialization of the TreeTraits class to the Octree tree type. More...

class	TreeTraits< RectangleTree< MetricType, StatisticType, MatType, RPlusTreeSplit< SplitPolicyType, SweepType >, DescentType, AuxiliaryInformationType > >
	Since the R+/R++ tree can not have overlapping children, we should define traits for the R+/R++ tree. More...

class	TreeTraits< RectangleTree< MetricType, StatisticType, MatType, SplitType, DescentType, AuxiliaryInformationType > >
	This is a specialization of the TreeType class to the RectangleTree tree type. More...

class	TreeTraits< SpillTree< MetricType, StatisticType, MatType, HyperplaneType, SplitType > >
	This is a specialization of the TreeType class to the SpillTree tree type. More...

class	UBTreeSplit
	Split a node into two parts according to the median address of points contained in the node. More...

class	VantagePointSplit
	The class splits a binary space partitioning tree node according to the median distance to the vantage point. More...

class	XTreeAuxiliaryInformation
	The XTreeAuxiliaryInformation class provides information specific to X trees for each node in a RectangleTree. More...

class	XTreeSplit
	A Rectangle Tree has new points inserted at the bottom. More...

Typedefs
template<typename MetricType >
using	AxisOrthogonalHyperplane = HyperplaneBase< bound::HRectBound< MetricType >, AxisParallelProjVector >
	AxisOrthogonalHyperplane represents a hyperplane orthogonal to an axis. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	BallTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::BallBound, MidpointSplit >
	A midpoint-split ball tree. More...

template<typename FitnessFunction >
using	BinaryDoubleNumericSplit = BinaryNumericSplit< FitnessFunction, double >

typedef boost::heap::priority_queue< CosineTree *, boost::heap::compare< CompareCosineNode > >	CosineNodeQueue

template<typename FitnessFunction = GiniGain, template< typename > class NumericSplitType = BestBinaryNumericSplit, template< typename > class CategoricalSplitType = AllCategoricalSplit, typename ElemType = double>
using	DecisionStump = DecisionTree< FitnessFunction, NumericSplitType, CategoricalSplitType, ElemType, false >
	Convenience typedef for decision stumps (single level decision trees). More...

template<typename TreeType >
using	DiscreteHilbertRTreeAuxiliaryInformation = HilbertRTreeAuxiliaryInformation< TreeType, DiscreteHilbertValue >
	The Hilbert R-tree, a variant of the R tree with an ordering along the Hilbert curve. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	HilbertRTree = RectangleTree< MetricType, StatisticType, MatType, HilbertRTreeSplit< 2 >, HilbertRTreeDescentHeuristic, DiscreteHilbertRTreeAuxiliaryInformation >

template<typename FitnessFunction >
using	HoeffdingDoubleNumericSplit = HoeffdingNumericSplit< FitnessFunction, double >
	Convenience typedef. More...

typedef StreamingDecisionTree< HoeffdingTree<> >	HoeffdingTreeType

template<typename MetricType >
using	Hyperplane = HyperplaneBase< bound::BallBound< MetricType >, ProjVector >
	Hyperplane represents a general hyperplane (not necessarily axis-orthogonal). More...

template<typename MetricType , typename StatisticType , typename MatType >
using	KDTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::HRectBound, MidpointSplit >
	The standard midpoint-split kd-tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	MaxRPTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::HRectBound, RPTreeMaxSplit >
	A max-split random projection tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	MeanSplitBallTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::BallBound, MeanSplit >
	A mean-split ball tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	MeanSplitKDTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::HRectBound, MeanSplit >
	A mean-split kd-tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	MeanSPTree = SpillTree< MetricType, StatisticType, MatType, AxisOrthogonalHyperplane, MeanSpaceSplit >
	A mean-split hybrid spill tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	NonOrtMeanSPTree = SpillTree< MetricType, StatisticType, MatType, Hyperplane, MeanSpaceSplit >
	A mean-split hybrid spill tree considering general splitting hyperplanes (not necessarily axis-orthogonal). More...

template<typename MetricType , typename StatisticType , typename MatType >
using	NonOrtSPTree = SpillTree< MetricType, StatisticType, MatType, Hyperplane, MidpointSpaceSplit >
	A hybrid spill tree considering general splitting hyperplanes (not necessarily axis-orthogonal). More...

template<typename MetricType , typename StatisticType , typename MatType >
using	RPlusPlusTree = RectangleTree< MetricType, StatisticType, MatType, RPlusTreeSplit< RPlusPlusTreeSplitPolicy, MinimalSplitsNumberSweep >, RPlusPlusTreeDescentHeuristic, RPlusPlusTreeAuxiliaryInformation >
	The R++ tree, a variant of the R+ tree with maximum buonding rectangles. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	RPlusTree = RectangleTree< MetricType, StatisticType, MatType, RPlusTreeSplit< RPlusTreeSplitPolicy, MinimalCoverageSweep >, RPlusTreeDescentHeuristic, NoAuxiliaryInformation >
	The R+ tree, a variant of the R tree that avoids overlapping rectangles. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	RPTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::HRectBound, RPTreeMeanSplit >
	A mean-split random projection tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	RStarTree = RectangleTree< MetricType, StatisticType, MatType, RStarTreeSplit, RStarTreeDescentHeuristic, NoAuxiliaryInformation >
	The R*-tree, a more recent variant of the R tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	RTree = RectangleTree< MetricType, StatisticType, MatType, RTreeSplit, RTreeDescentHeuristic, NoAuxiliaryInformation >
	An implementation of the R tree that satisfies the TreeType policy API. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	SPTree = SpillTree< MetricType, StatisticType, MatType, AxisOrthogonalHyperplane, MidpointSpaceSplit >
	The hybrid spill tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	StandardCoverTree = CoverTree< MetricType, StatisticType, MatType, FirstPointIsRoot >
	The standard cover tree, as detailed in the original cover tree paper: More...

template<typename MetricType , typename StatisticType , typename MatType >
using	UBTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::CellBound, UBTreeSplit >
	The Universal B-tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	VPTree = BinarySpaceTree< MetricType, StatisticType, MatType, bound::HollowBallBound, VPTreeSplit >

template<typename BoundType , typename MatType = arma::mat>
using	VPTreeSplit = VantagePointSplit< BoundType, MatType, 100 >
	The vantage point tree (which is also called the metric tree. More...

template<typename MetricType , typename StatisticType , typename MatType >
using	XTree = RectangleTree< MetricType, StatisticType, MatType, XTreeSplit, RTreeDescentHeuristic, XTreeAuxiliaryInformation >
	The X-tree, a variant of the R tree with supernodes. More...

Variables
const double	MAX_OVERLAP = 0.2
	The X-tree paper says that a maximum allowable overlap of 20% works well. More...

Detailed Description

Trees and tree-building procedures.

Typedef Documentation

template<typename MetricType >

using mlpack::tree::AxisOrthogonalHyperplane = typedef HyperplaneBase<bound::HRectBound<MetricType>, AxisParallelProjVector>

AxisOrthogonalHyperplane represents a hyperplane orthogonal to an axis.

Definition at line 145 of file hyperplane.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::BallTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::BallBound, MidpointSplit>

A midpoint-split ball tree.

This tree holds its points only in the leaves, similar to the KDTree and MeanSplitKDTree. However, the bounding shape of each node is a ball, not a hyper-rectangle. This can make the ball tree advantageous in some higher-dimensional situations and for some datasets. The tree construction algorithm here is the same as Omohundro's 'K-d construction algorithm', except the splitting value is the midpoint, not the median. This can result in trees that better reflect the data, although they may be unbalanced.

@techreport{omohundro1989five,
  author={S.M. Omohundro},
  title={Five balltree construction algorithms},
  year={1989},
  institution={University of California, Berkeley International Computer
      Science Institute Technical Reports},
  number={TR-89-063}
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, KDTree, MeanSplitBallTree

Definition at line 112 of file typedef.hpp.

template<typename FitnessFunction >

using mlpack::tree::BinaryDoubleNumericSplit = typedef BinaryNumericSplit<FitnessFunction, double>

Definition at line 128 of file binary_numeric_split.hpp.

typedef boost::heap::priority_queue<CosineTree*, boost::heap::compare<CompareCosineNode> > mlpack::tree::CosineNodeQueue

Definition at line 23 of file cosine_tree.hpp.

template<typename FitnessFunction = GiniGain, template< typename > class NumericSplitType = BestBinaryNumericSplit, template< typename > class CategoricalSplitType = AllCategoricalSplit, typename ElemType = double>

using mlpack::tree::DecisionStump = typedef DecisionTree<FitnessFunction, NumericSplitType, CategoricalSplitType, ElemType, false>

Convenience typedef for decision stumps (single level decision trees).

Definition at line 275 of file decision_tree.hpp.

template<typename TreeType >

using mlpack::tree::DiscreteHilbertRTreeAuxiliaryInformation = typedef HilbertRTreeAuxiliaryInformation<TreeType,DiscreteHilbertValue>

The Hilbert R-tree, a variant of the R tree with an ordering along the Hilbert curve.

This template typedef satisfies the TreeType policy API.

@inproceedings{kamel1994r,
  author = {Kamel, Ibrahim and Faloutsos, Christos},
  title = {Hilbert R-tree: An Improved R-tree Using Fractals},
  booktitle = {Proceedings of the 20th International Conference on Very Large Data Bases},
  series = {VLDB '94},
  year = {1994},
  isbn = {1-55860-153-8},
  pages = {500--509},
  numpages = {10},
  url = {http://dl.acm.org/citation.cfm?id=645920.673001},
  acmid = {673001},
  publisher = {Morgan Kaufmann Publishers Inc.},
  address = {San Francisco, CA, USA}
}

See also: The TreeType policy in mlpack, RTree, DiscreteHilbertRTree

Definition at line 128 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::HilbertRTree = typedef RectangleTree<MetricType, StatisticType, MatType, HilbertRTreeSplit<2>, HilbertRTreeDescentHeuristic, DiscreteHilbertRTreeAuxiliaryInformation>

Definition at line 136 of file typedef.hpp.

template<typename FitnessFunction >

using mlpack::tree::HoeffdingDoubleNumericSplit = typedef HoeffdingNumericSplit<FitnessFunction, double>

Convenience typedef.

Definition at line 148 of file hoeffding_numeric_split.hpp.

typedef StreamingDecisionTree<HoeffdingTree<> > mlpack::tree::HoeffdingTreeType

Definition at line 21 of file typedef.hpp.

template<typename MetricType >

using mlpack::tree::Hyperplane = typedef HyperplaneBase<bound::BallBound<MetricType>, ProjVector>

Hyperplane represents a general hyperplane (not necessarily axis-orthogonal).

Definition at line 151 of file hyperplane.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::KDTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::HRectBound, MidpointSplit>

The standard midpoint-split kd-tree.

This is not the original formulation by Bentley but instead the later formulation by Deng and Moore, which only holds points in the leaves of the tree. When recursively splitting nodes, the KDTree class select the dimension with maximum variance to split on, and picks the midpoint of the range in that dimension as the value on which to split nodes.

For more information, see the following papers.

@article{bentley1975multidimensional,
  title={Multidimensional binary search trees used for associative searching},
  author={Bentley, J.L.},
  journal={Communications of the ACM},
  volume={18},
  number={9},
  pages={509--517},
  year={1975},
  publisher={ACM}
}
@inproceedings{deng1995multiresolution,
  title={Multiresolution instance-based learning},
  author={Deng, K. and Moore, A.W.},
  booktitle={Proceedings of the 1995 International Joint Conference on AI
      (IJCAI-95)},
  pages={1233--1239},
  year={1995}
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, MeanSplitKDTree

Definition at line 63 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::MaxRPTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::HRectBound, RPTreeMaxSplit>

A max-split random projection tree.

When recursively splitting nodes, the MaxSplitRPTree class selects a random hyperplane and splits a node by the hyperplane. The tree holds points in leaf nodes. In contrast to the k-d tree, children of a MaxSplitRPTree node may overlap.

@inproceedings{dasgupta2008,
  author = {Dasgupta, Sanjoy and Freund, Yoav},
  title = {Random Projection Trees and Low Dimensional Manifolds},
  booktitle = {Proceedings of the Fortieth Annual ACM Symposium on Theory of
      Computing},
  series = {STOC '08},
  year = {2008},
  pages = {537--546},
  numpages = {10},
  publisher = {ACM},
  address = {New York, NY, USA},
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, BallTree, MeanSplitKDTree

Definition at line 232 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::MeanSplitBallTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::BallBound, MeanSplit>

A mean-split ball tree.

This tree, like the BallTree, holds its points only in the leaves. The tree construction algorithm here is the same as Omohundro's 'K-dc onstruction algorithm', except the splitting value is the mean, not the median. This can result in trees that better reflect the data, although they may be unbalanced.

@techreport{omohundro1989five,
  author={S.M. Omohundro},
  title={Five balltree construction algorithms},
  year={1989},
  institution={University of California, Berkeley International Computer
      Science Institute Technical Reports},
  number={TR-89-063}
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, BallTree, MeanSplitKDTree

Definition at line 141 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::MeanSplitKDTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::HRectBound, MeanSplit>

A mean-split kd-tree.

This is the same as the KDTree, but this particular implementation will use the mean of the data in the split dimension as the value on which to split, instead of the midpoint. This can sometimes give better performance, but it is not always clear which type of tree is best.

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, KDTree

Definition at line 80 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::MeanSPTree = typedef SpillTree<MetricType, StatisticType, MatType, AxisOrthogonalHyperplane, MeanSpaceSplit>

A mean-split hybrid spill tree.

This is the same as the SPTree, but this particular implementation will use the mean of the data in the split dimension as the value on which to split, instead of the midpoint. This can sometimes give better performance, but it is not always clear which type of tree is best.

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, SpillTree, SPTree

Definition at line 80 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::NonOrtMeanSPTree = typedef SpillTree<MetricType, StatisticType, MatType, Hyperplane, MeanSpaceSplit>

A mean-split hybrid spill tree considering general splitting hyperplanes (not necessarily axis-orthogonal).

This is the same as the NonOrtSPTree, but this particular implementation will use the mean of the data in the split projection as the value on which to split, instead of the midpoint. This can sometimes give better performance, but it is not always clear which type of tree is best.

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, SpillTree, MeanSPTree, NonOrtSPTree

Definition at line 119 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::NonOrtSPTree = typedef SpillTree<MetricType, StatisticType, MatType, Hyperplane, MidpointSpaceSplit>

A hybrid spill tree considering general splitting hyperplanes (not necessarily axis-orthogonal).

This particular implementation will consider the midpoint of the projection of the data in the vector determined by the farthest pair of points. This can sometimes give better performance, but generally it doesn't because it takes O(d) to calculate the projection of the query point when deciding which node to traverse, while when using a axis-orthogonal hyperplane, as SPTree does, we can do it in O(1).

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, SpillTree, SPTree

Definition at line 100 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::RPlusPlusTree = typedef RectangleTree<MetricType, StatisticType, MatType, RPlusTreeSplit<RPlusPlusTreeSplitPolicy, MinimalSplitsNumberSweep>, RPlusPlusTreeDescentHeuristic, RPlusPlusTreeAuxiliaryInformation>

The R++ tree, a variant of the R+ tree with maximum buonding rectangles.

This template typedef satisfies the TreeType policy API.

@inproceedings{sumak2014r,
  author = {{\v{S}}um{\'a}k, Martin and Gursk{\'y}, Peter},
  title = {R++-Tree: An Efficient Spatial Access Method for Highly Redundant
     Point Data},
  booktitle = {New Trends in Databases and Information Systems: 17th East
     European Conference on Advances in Databases and Information Systems},
  year = {2014},
  isbn = {978-3-319-01863-8},
  pages = {37--44},
  publisher = {Springer International Publishing},
}

See also: The TreeType policy in mlpack, RTree, RTree, RPlusTree, RPlusPlusTree

Definition at line 196 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::RPlusTree = typedef RectangleTree<MetricType, StatisticType, MatType, RPlusTreeSplit<RPlusTreeSplitPolicy, MinimalCoverageSweep>, RPlusTreeDescentHeuristic, NoAuxiliaryInformation>

The R+ tree, a variant of the R tree that avoids overlapping rectangles.

The implementation is modified from the original paper implementation. This template typedef satisfies the TreeType policy API.

@inproceedings{sellis1987r,
  author = {Sellis, Timos K. and Roussopoulos, Nick and Faloutsos, Christos},
  title = {The R+-Tree: A Dynamic Index for Multi-Dimensional Objects},
  booktitle = {Proceedings of the 13th International Conference on Very
     Large Data Bases},
  series = {VLDB '87},
  year = {1987},
  isbn = {0-934613-46-X},
  pages = {507--518},
  numpages = {12},
  publisher = {Morgan Kaufmann Publishers Inc.},
  address = {San Francisco, CA, USA},
}

See also: The TreeType policy in mlpack, RTree, RTree, RPlusTree

Definition at line 168 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::RPTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::HRectBound, RPTreeMeanSplit>

A mean-split random projection tree.

When recursively splitting nodes, the RPTree class may perform one of two different kinds of split. Depending on the diameter and the average distance between points, the node may be split by a random hyperplane or according to the distance from the mean point. The tree holds points in leaf nodes. In contrast to the k-d tree, children of a MaxSplitRPTree node may overlap.

@inproceedings{dasgupta2008,
  author = {Dasgupta, Sanjoy and Freund, Yoav},
  title = {Random Projection Trees and Low Dimensional Manifolds},
  booktitle = {Proceedings of the Fortieth Annual ACM Symposium on Theory of
      Computing},
  series = {STOC '08},
  year = {2008},
  pages = {537--546},
  numpages = {10},
  publisher = {ACM},
  address = {New York, NY, USA},
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, BallTree, MeanSplitKDTree

Definition at line 266 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::RStarTree = typedef RectangleTree<MetricType, StatisticType, MatType, RStarTreeSplit, RStarTreeDescentHeuristic, NoAuxiliaryInformation>

The R*-tree, a more recent variant of the R tree.

This template typedef satisfies the TreeType policy API.

@inproceedings{beckmann1990r,
  title={The R*-tree: an efficient and robust access method for points and
      rectangles},
  author={Beckmann, N. and Kriegel, H.-P. and Schneider, R. and Seeger, B.},
  booktitle={Proceedings of the 1990 ACM SIGMOD International Conference on
      Management of Data (SIGMOD '90)},
  volume={19},
  number={2},
  year={1990},
  publisher={ACM}
}

See also: The TreeType policy in mlpack, RTree

Definition at line 75 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::RTree = typedef RectangleTree<MetricType, StatisticType, MatType, RTreeSplit, RTreeDescentHeuristic, NoAuxiliaryInformation>

An implementation of the R tree that satisfies the TreeType policy API.

This is the same R-tree structure as proposed by Guttman:

@inproceedings{guttman1984r,
  title={R-trees: a dynamic index structure for spatial searching},
  author={Guttman, A.},
  booktitle={Proceedings of the 1984 ACM SIGMOD International Conference on
      Management of Data (SIGMOD '84)},
  volume={14},
  number={2},
  year={1984},
  publisher={ACM}
}

See also: The TreeType policy in mlpack, RStarTree

Definition at line 47 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::SPTree = typedef SpillTree<MetricType, StatisticType, MatType, AxisOrthogonalHyperplane, MidpointSpaceSplit>

The hybrid spill tree.

It is a variant of metric-trees in which the children of a node can "spill over" onto each other, and contain shared datapoints.

When recursively splitting nodes, the SPTree class select the dimension with maximum width to split on, and picks the midpoint of the range in that dimension as the value on which to split nodes.

In each case a "overlapping buffer" is defined, included points at a distance less than tau from the decision boundary defined by the midpoint.

For each node, we first split the points considering the overlapping buffer. If either of its children contains more than rho fraction of the total points we undo the overlapping splitting. Instead a conventional partition is used. In this way, we can ensure that each split reduces the number of points of a node by at least a constant factor.

For more information, see the following paper.

@inproceedings{
  author = {Ting Liu, Andrew W. Moore, Alexander Gray and Ke Yang},
  title = {An Investigation of Practical Approximate Nearest Neighbor
    Algorithms},
  booktitle = {Advances in Neural Information Processing Systems 17},
  year = {2005},
  pages = {825--832}
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, SpillTree, MeanSPTree

Definition at line 62 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::StandardCoverTree = typedef CoverTree<MetricType, StatisticType, MatType, FirstPointIsRoot>

The standard cover tree, as detailed in the original cover tree paper:

@inproceedings{
  author={Beygelzimer, A. and Kakade, S. and Langford, J.},
  title={Cover trees for nearest neighbor},
  booktitle={Proceedings of the 23rd International Conference on Machine
      Learning (ICML 2006)},
  pages={97--104},
  year={2006}
}

This template typedef satisfies the requirements of the TreeType API.

See also: The TreeType policy in mlpack, CoverTree

Definition at line 42 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::UBTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::CellBound, UBTreeSplit>

The Universal B-tree.

When recursively splitting nodes, the class calculates addresses of all points and splits each node according to the median address. Children may overlap since the implementation of a tighter bound requires a lot of arithmetic operations. In order to get a tighter bound increase the CellBound::maxNumBounds constant.

@inproceedings{bayer1997,
  author = {Bayer, Rudolf},
  title = {The Universal B-Tree for Multidimensional Indexing: General
      Concepts},
  booktitle = {Proceedings of the International Conference on Worldwide
      Computing and Its Applications},
  series = {WWCA '97},
  year = {1997},
  isbn = {3-540-63343-X},
  pages = {198--209},
  numpages = {12},
  publisher = {Springer-Verlag},
  address = {London, UK, UK},
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, BallTree, MeanSplitKDTree

Definition at line 301 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::VPTree = typedef BinarySpaceTree<MetricType, StatisticType, MatType, bound::HollowBallBound, VPTreeSplit>

Definition at line 199 of file typedef.hpp.

template<typename BoundType , typename MatType = arma::mat>

using mlpack::tree::VPTreeSplit = typedef VantagePointSplit<BoundType, MatType, 100>

The vantage point tree (which is also called the metric tree.

Vantage point trees and metric trees were invented independently by Yianilos an Uhlmann) is a kind of the binary space tree. When recursively splitting nodes, the VPTree class selects the vantage point and splits the node according to the distance to this point. Thus, points that are closer to the vantage point form the inner subtree. Other points form the outer subtree. The vantage point is contained in the first (inner) node.

This implementation differs from the original algorithms. Namely, vantage points are not contained in intermediate nodes. The tree has points only in the leaves of the tree.

For more information, see the following papers.

@inproceedings{yianilos1993vptrees,
  author = {Yianilos, Peter N.},
  title = {Data Structures and Algorithms for Nearest Neighbor Search in
      General Metric Spaces},
  booktitle = {Proceedings of the Fourth Annual ACM-SIAM Symposium on
      Discrete Algorithms},
  series = {SODA '93},
  year = {1993},
  isbn = {0-89871-313-7},
  pages = {311--321},
  numpages = {11},
  publisher = {Society for Industrial and Applied Mathematics},
  address = {Philadelphia, PA, USA}
}
@article{uhlmann1991metrictrees,
  author = {Jeffrey K. Uhlmann},
  title = {Satisfying general proximity / similarity queries with metric
      trees},
  journal = {Information Processing Letters},
  volume = {40},
  number = {4},
  pages = {175 - 179},
  year = {1991},
}

This template typedef satisfies the TreeType policy API.

See also: The TreeType policy in mlpack, BinarySpaceTree, VantagePointTree, VPTree

Definition at line 192 of file typedef.hpp.

template<typename MetricType , typename StatisticType , typename MatType >

using mlpack::tree::XTree = typedef RectangleTree<MetricType, StatisticType, MatType, XTreeSplit, RTreeDescentHeuristic, XTreeAuxiliaryInformation>

The X-tree, a variant of the R tree with supernodes.

This template typedef satisfies the TreeType policy API.

@inproceedings{berchtold1996r,
  title = {The X-Tree: An Index Structure for High--Dimensional Data},
  author = {Berchtold, Stefan and Keim, Daniel A. and Kriegel, Hans-Peter},
  booktitle = {Proc. 22th Int. Conf. on Very Large Databases (VLDB'96), Bombay, India},
  editor = {Vijayaraman, T. and Buchmann, Alex and Mohan, C. and Sarda, N.},
  pages = {28--39},
  year = {1996},
  publisher = {Morgan Kaufmann}
}

See also: The TreeType policy in mlpack, RTree, RStarTree

Definition at line 101 of file typedef.hpp.

Variable Documentation

const double mlpack::tree::MAX_OVERLAP = 0.2

The X-tree paper says that a maximum allowable overlap of 20% works well.

This code should eventually be refactored so as to avoid polluting mlpack::tree with this random double.

Definition at line 29 of file x_tree_split.hpp.

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