A density estimation tree is similar to both a decision tree and a space partitioning tree (like a kd-tree). More...

Public Types
typedef MatType::elem_type	ElemType
	The actual, underlying type we're working with. More...

typedef arma::Col< ElemType >	StatType
	The statistic type we are holding. More...

typedef MatType::vec_type	VecType
	The type of vector we are using. More...

Public Member Functions
	DTree ()
	Create an empty density estimation tree. More...

	DTree (const DTree &obj)
	Create a tree that is the copy of the given tree. More...

	DTree (DTree &&obj)
	Create a tree by taking ownership of another tree (move constructor). More...

	DTree (const StatType &maxVals, const StatType &minVals, const size_t totalPoints)
	Create a density estimation tree with the given bounds and the given number of total points. More...

	DTree (MatType &data)
	Create a density estimation tree on the given data. More...

	DTree (const StatType &maxVals, const StatType &minVals, const size_t start, const size_t end, const double logNegError)
	Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end and the specified error. More...

	DTree (const StatType &maxVals, const StatType &minVals, const size_t totalPoints, const size_t start, const size_t end)
	Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end, and calculating the error with the total number of points given. More...

	~DTree ()
	Clean up memory allocated by the tree. More...

double	AlphaUpper () const
	Return the upper part of the alpha sum. More...

TagType	BucketTag () const
	Return the current bucket's ID, if leaf, or -1 otherwise. More...

DTree &	Child (const size_t child) const
	Return the specified child (0 will be left, 1 will be right). More...

DTree *&	ChildPtr (const size_t child)

double	ComputeValue (const VecType &query) const
	Compute the logarithm of the density estimate of a given query point. More...

void	ComputeVariableImportance (arma::vec &importances) const
	Compute the variable importance of each dimension in the learned tree. More...

size_t	End () const
	Return the first index of a point not contained in this node. More...

TagType	FindBucket (const VecType &query) const
	Return the tag of the leaf containing the query. More...

double	Grow (MatType &data, arma::Col< size_t > &oldFromNew, const bool useVolReg=false, const size_t maxLeafSize=10, const size_t minLeafSize=5)
	Greedily expand the tree. More...

DTree *	Left () const
	Return the left child. More...

double	LogNegativeError (const size_t totalPoints) const
	Compute the log-negative-error for this point, given the total number of points in the dataset. More...

double	LogNegError () const
	Return the log negative error of this node. More...

double	LogVolume () const
	Return the inverse of the volume of this node. More...

const StatType &	MaxVals () const
	Return the maximum values. More...

const StatType &	MinVals () const
	Return the minimum values. More...

size_t	NumChildren () const
	Return the number of children in this node. More...

DTree &	operator= (const DTree &obj)
	Copy the given tree. More...

DTree &	operator= (DTree &&obj)
	Take ownership of the given tree (move operator). More...

double	PruneAndUpdate (const double oldAlpha, const size_t points, const bool useVolReg=false)
	Perform alpha pruning on a tree. More...

double	Ratio () const
	Return the ratio of points in this node to the points in the whole dataset. More...

DTree *	Right () const
	Return the right child. More...

bool	Root () const
	Return whether or not this is the root of the tree. More...

template < typename Archive >
void	serialize (Archive &ar, const unsigned int)
	Serialize the density estimation tree. More...

size_t	SplitDim () const
	Return the split dimension of this node. More...

ElemType	SplitValue () const
	Return the split value of this node. More...

size_t	Start () const
	Return the starting index of points contained in this node. More...

size_t	SubtreeLeaves () const
	Return the number of leaves which are descendants of this node. More...

double	SubtreeLeavesLogNegError () const
	Return the log negative error of all descendants of this node. More...

TagType	TagTree (const TagType &tag=0, bool everyNode=false)
	Index the buckets for possible usage later; this results in every leaf in the tree having a specific tag (accessible with BucketTag()). More...

bool	WithinRange (const VecType &query) const
	Return whether a query point is within the range of this node. More...

Detailed Description

template
<
typename
MatType
=
arma::mat
,
typename
TagType
=
int
>

class mlpack::det::DTree< MatType, TagType >

A density estimation tree is similar to both a decision tree and a space partitioning tree (like a kd-tree).

Each leaf represents a constant-density hyper-rectangle. The tree is constructed in such a way as to minimize the integrated square error between the probability distribution of the tree and the observed probability distribution of the data. Because the tree is similar to a decision tree, the density estimation tree can provide very fast density estimates for a given point.

For more information, see the following paper:

@incollection{ram2011,
  author = {Ram, Parikshit and Gray, Alexander G.},
  title = {Density estimation trees},
  booktitle = {{Proceedings of the 17th ACM SIGKDD International Conference
      on Knowledge Discovery and Data Mining}},
  series = {KDD '11},
  year = {2011},
  pages = {627--635}
}

Definition at line 46 of file dtree.hpp.

Member Typedef Documentation

◆ ElemType

typedef MatType::elem_type ElemType

The actual, underlying type we're working with.

Definition at line 50 of file dtree.hpp.

◆ StatType

typedef arma::Col<ElemType> StatType

The statistic type we are holding.

Definition at line 54 of file dtree.hpp.

◆ VecType

typedef MatType::vec_type VecType

The type of vector we are using.

Definition at line 52 of file dtree.hpp.

Constructor & Destructor Documentation

◆ DTree() [1/7]

DTree ( )

Create an empty density estimation tree.

◆ DTree() [2/7]

DTree ( const DTree< MatType, TagType > & obj )

Create a tree that is the copy of the given tree.

Parameters

obj	Tree to copy.

◆ DTree() [3/7]

DTree ( DTree< MatType, TagType > && obj )

Create a tree by taking ownership of another tree (move constructor).

Parameters

obj	Tree to take ownership of.

◆ DTree() [4/7]

DTree	(	const StatType &	maxVals,
		const StatType &	minVals,
		const size_t	totalPoints
	)

Create a density estimation tree with the given bounds and the given number of total points.

Children will not be created.

Parameters

maxVals	Maximum values of the bounding box.
minVals	Minimum values of the bounding box.
totalPoints	Total number of points in the dataset.

◆ DTree() [5/7]

DTree ( MatType & data )

Create a density estimation tree on the given data.

Children will be created following the procedure outlined in the paper. The data will be modified; it will be reordered similar to the way BinarySpaceTree modifies datasets.

Parameters

data	Dataset to build tree on.

◆ DTree() [6/7]

DTree	(	const StatType &	maxVals,
		const StatType &	minVals,
		const size_t	start,
		const size_t	end,
		const double	logNegError
	)

Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end and the specified error.

Children of this node will not be created recursively.

Parameters

maxVals	Upper bound of bounding box.
minVals	Lower bound of bounding box.
start	Start of points represented by this node in the data matrix.
end	End of points represented by this node in the data matrix.
error	log-negative error of this node.

◆ DTree() [7/7]

DTree	(	const StatType &	maxVals,
		const StatType &	minVals,
		const size_t	totalPoints,
		const size_t	start,
		const size_t	end
	)

Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end, and calculating the error with the total number of points given.

Children of this node will not be created recursively.

Parameters

maxVals	Upper bound of bounding box.
minVals	Lower bound of bounding box.
start	Start of points represented by this node in the data matrix.
end	End of points represented by this node in the data matrix.

◆ ~DTree()

~DTree ( )

Clean up memory allocated by the tree.

Member Function Documentation

◆ AlphaUpper()

double AlphaUpper ( ) const

inline

Return the upper part of the alpha sum.

Definition at line 306 of file dtree.hpp.

◆ BucketTag()

TagType BucketTag ( ) const

inline

Return the current bucket's ID, if leaf, or -1 otherwise.

Definition at line 308 of file dtree.hpp.

◆ Child()

DTree& Child ( const size_t child ) const

inline

Return the specified child (0 will be left, 1 will be right).

If the index is greater than 1, this will return the right child.

Parameters

child Index of child to return.

Definition at line 318 of file dtree.hpp.

◆ ChildPtr()

DTree*& ChildPtr ( const size_t child )

inline

Definition at line 320 of file dtree.hpp.

◆ ComputeValue()

double ComputeValue ( const VecType & query ) const

Compute the logarithm of the density estimate of a given query point.

Parameters

query Point to estimate density of.

◆ ComputeVariableImportance()

void ComputeVariableImportance ( arma::vec & importances ) const

Compute the variable importance of each dimension in the learned tree.

Parameters

importances Vector to store the calculated importances in.

◆ End()

size_t End ( ) const

inline

Return the first index of a point not contained in this node.

Definition at line 283 of file dtree.hpp.

◆ FindBucket()

TagType FindBucket ( const VecType & query ) const

Return the tag of the leaf containing the query.

This is useful for generating class memberships.

Parameters

query Query to search for.

◆ Grow()

double Grow	(	MatType &	data,
		arma::Col< size_t > &	oldFromNew,
		const bool	useVolReg = `false`,
		const size_t	maxLeafSize = `10`,
		const size_t	minLeafSize = `5`
	)

Greedily expand the tree.

The points in the dataset will be reordered during tree growth.

Parameters

data	Dataset to build tree on.
oldFromNew	Mappings from old points to new points.
useVolReg	If true, volume regularization is used.
maxLeafSize	Maximum size of a leaf.
minLeafSize	Minimum size of a leaf.

◆ Left()

DTree* Left ( ) const

inline

Return the left child.

Definition at line 300 of file dtree.hpp.

◆ LogNegativeError()

double LogNegativeError ( const size_t totalPoints ) const

Compute the log-negative-error for this point, given the total number of points in the dataset.

Parameters

totalPoints Total number of points in the dataset.

◆ LogNegError()

double LogNegError ( ) const

inline

Return the log negative error of this node.

Definition at line 289 of file dtree.hpp.

◆ LogVolume()

double LogVolume ( ) const

inline

Return the inverse of the volume of this node.

Definition at line 298 of file dtree.hpp.

◆ MaxVals()

const StatType& MaxVals ( ) const

inline

Return the maximum values.

Definition at line 323 of file dtree.hpp.

◆ MinVals()

const StatType& MinVals ( ) const

inline

Return the minimum values.

Definition at line 326 of file dtree.hpp.

References DTree< MatType, TagType >::serialize().

◆ NumChildren()

size_t NumChildren ( ) const

inline

Return the number of children in this node.

Definition at line 310 of file dtree.hpp.

◆ operator=() [1/2]

DTree& operator= ( const DTree< MatType, TagType > & obj )

Copy the given tree.

Parameters

obj	Tree to copy.

◆ operator=() [2/2]

DTree& operator= ( DTree< MatType, TagType > && obj )

Take ownership of the given tree (move operator).

Parameters

obj	Tree to take ownership of.

◆ PruneAndUpdate()

double PruneAndUpdate	(	const double	oldAlpha,
		const size_t	points,
		const bool	useVolReg = `false`
	)

Perform alpha pruning on a tree.

Returns the new value of alpha.

Parameters

oldAlpha	Old value of alpha.
points	Total number of points in dataset.
useVolReg	If true, volume regularization is used.

Returns: New value of alpha.

◆ Ratio()

double Ratio ( ) const

inline

Return the ratio of points in this node to the points in the whole dataset.

Definition at line 296 of file dtree.hpp.

◆ Right()

DTree* Right ( ) const

inline

Return the right child.

Definition at line 302 of file dtree.hpp.

◆ Root()

bool Root ( ) const

inline

Return whether or not this is the root of the tree.

Definition at line 304 of file dtree.hpp.

◆ serialize()

void serialize	(	Archive &	ar,
		const unsigned	int
	)

Serialize the density estimation tree.

Referenced by DTree< MatType, TagType >::MinVals().

◆ SplitDim()

size_t SplitDim ( ) const

inline

Return the split dimension of this node.

Definition at line 285 of file dtree.hpp.

◆ SplitValue()

ElemType SplitValue ( ) const

inline

Return the split value of this node.

Definition at line 287 of file dtree.hpp.

◆ Start()

size_t Start ( ) const

inline

Return the starting index of points contained in this node.

Definition at line 281 of file dtree.hpp.

◆ SubtreeLeaves()

size_t SubtreeLeaves ( ) const

inline

Return the number of leaves which are descendants of this node.

Definition at line 293 of file dtree.hpp.

◆ SubtreeLeavesLogNegError()

double SubtreeLeavesLogNegError ( ) const

inline

Return the log negative error of all descendants of this node.

Definition at line 291 of file dtree.hpp.

◆ TagTree()

TagType TagTree	(	const TagType &	tag = `0`,
		bool	everyNode = `false`
	)

Index the buckets for possible usage later; this results in every leaf in the tree having a specific tag (accessible with BucketTag()).

This function calls itself recursively. The tag is incremented with operator++(), so any TagType overriding it will do.

Parameters

tag	Tag for the next leaf; leave at 0 for the initial call.
everyNodde	Whether to increment on every node, not just leaves.

◆ WithinRange()

bool WithinRange ( const VecType & query ) const

Return whether a query point is within the range of this node.

The documentation for this class was generated from the following file:

src/mlpack/methods/det/dtree.hpp

Public Types

Public Member Functions

Detailed Description

template<typenameMatType=arma::mat,typenameTagType=int> class mlpack::det::DTree< MatType, TagType >

Member Typedef Documentation

◆ ElemType

◆ StatType

◆ VecType

Constructor & Destructor Documentation

◆ DTree() [1/7]

◆ DTree() [2/7]

◆ DTree() [3/7]

◆ DTree() [4/7]

◆ DTree() [5/7]

◆ DTree() [6/7]

◆ DTree() [7/7]

◆ ~DTree()

Member Function Documentation

◆ AlphaUpper()

◆ BucketTag()

◆ Child()

◆ ChildPtr()

◆ ComputeValue()

◆ ComputeVariableImportance()

◆ End()

◆ FindBucket()

◆ Grow()

◆ Left()

◆ LogNegativeError()

◆ LogNegError()

◆ LogVolume()

◆ MaxVals()

◆ MinVals()

◆ NumChildren()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PruneAndUpdate()

◆ Ratio()

◆ Right()

◆ Root()

◆ serialize()

◆ SplitDim()

◆ SplitValue()

◆ Start()

◆ SubtreeLeaves()

◆ SubtreeLeavesLogNegError()

◆ TagTree()

◆ WithinRange()

template
<
typename
MatType
=
arma::mat
,
typename
TagType
=
int
>

class mlpack::det::DTree< MatType, TagType >