Public Member Functions
	CosineTree (const arma::mat &dataset)
	CosineTree constructor for the root node of the tree. More...

	CosineTree (CosineTree &parentNode, const std::vector< size_t > &subIndices)
	CosineTree constructor for nodes other than the root node of the tree. More...

	CosineTree (const arma::mat &dataset, const double epsilon, const double delta)
	Construct the CosineTree and the basis for the given matrix, and passed 'epsilon' and 'delta' parameters. More...

	~CosineTree ()
	Clean up the CosineTree: release allocated memory (including children). More...

void	BasisVector (arma::vec &bVector)
	Set the basis vector of the node. More...

arma::vec &	BasisVector ()
	Get the basis vector of the node. More...

size_t	BinarySearch (arma::vec &cDistribution, double value, size_t start, size_t end)
	Sample a column based on the cumulative Length-Squared distribution of the cosine node, and a randomly generated value in the range [0, 1]. More...

void	CalculateCentroid ()
	Calculate centroid of the columns present in the node. More...

void	CalculateCosines (arma::vec &cosines)
	Calculate cosines of the columns present in the node, with respect to the sampled splitting point. More...

arma::vec &	Centroid ()
	Get pointer to the centroid vector. More...

size_t	ColumnSampleLS ()
	Sample a point from the Length-Squared distribution of the cosine node. More...

void	ColumnSamplesLS (std::vector< size_t > &sampledIndices, arma::vec &probabilities, size_t numSamples)
	Sample 'numSamples' points from the Length-Squared distribution of the cosine node. More...

void	ConstructBasis (CosineNodeQueue &treeQueue)
	Constructs the final basis matrix, after the cosine tree construction. More...

void	CosineNodeSplit ()
	This function splits the cosine node into two children based on the cosines of the columns contained in the node, with respect to the sampled splitting point. More...

double	FrobNormSquared () const
	Get the Frobenius norm squared of columns in the node. More...

const arma::mat &	GetDataset () const
	Get pointer to the dataset matrix. More...

void	GetFinalBasis (arma::mat &finalBasis)
	Returns the basis of the constructed subspace. More...

void	L2Error (const double error)
	Set the Monte Carlo error. More...

double	L2Error () const
	Get the Monte Carlo error. More...

CosineTree *	Left () const
	Get pointer to the left child of the node. More...

CosineTree *&	Left ()
	Modify the pointer to the left child of the node. More...

void	ModifiedGramSchmidt (CosineNodeQueue &treeQueue, arma::vec &centroid, arma::vec &newBasisVector, arma::vec *addBasisVector=NULL)
	Calculates the orthonormalization of the passed centroid, with respect to the current vector subspace. More...

double	MonteCarloError (CosineTree node, CosineNodeQueue &treeQueue, arma::vec addBasisVector1=NULL, arma::vec *addBasisVector2=NULL)
	Estimates the squared error of the projection of the input node's matrix onto the current vector subspace. More...

size_t	NumColumns () const
	Get number of columns of input matrix in the node. More...

CosineTree *	Parent () const
	Get pointer to the parent node. More...

CosineTree *&	Parent ()
	Modify the pointer to the parent node. More...

CosineTree *	Right () const
	Get pointer to the right child of the node. More...

CosineTree *&	Right ()
	Modify the pointer to the left child of the node. More...

size_t	SplitPointIndex () const
	Get the column index of split point of the node. More...

std::vector< size_t > &	VectorIndices ()
	Get the indices of columns in the node. More...

Private Attributes
arma::mat	basis
	Subspace basis of the input dataset. More...

arma::vec	basisVector
	Orthonormalized basis vector of the node. More...

arma::vec	centroid
	Centroid of columns of input matrix in the node. More...

const arma::mat &	dataset
	Matrix for which cosine tree is constructed. More...

double	delta
	Cumulative probability for Monte Carlo error lower bound. More...

double	frobNormSquared
	Frobenius norm squared of columns in the node. More...

std::vector< size_t >	indices
	Indices of columns of input matrix in the node. More...

double	l2Error
	Monte Carlo error for this node. More...

arma::vec	l2NormsSquared
	L2-norm squared of columns in the node. More...

CosineTree *	left
	Left child of the node. More...

size_t	numColumns
	Number of columns of input matrix in the node. More...

CosineTree *	parent
	Parent of the node. More...

CosineTree *	right
	Right child of the node. More...

size_t	splitPointIndex
	Index of split point of cosine node. More...

Detailed Description

Definition at line 29 of file cosine_tree.hpp.

Constructor & Destructor Documentation

mlpack::tree::CosineTree::CosineTree ( const arma::mat & dataset )

CosineTree constructor for the root node of the tree.

It initializes the necessary variables required for splitting of the node, and building the tree further. It takes a pointer to the input matrix and calculates the relevant variables using it.

Parameters

dataset Matrix for which cosine tree is constructed.

mlpack::tree::CosineTree::CosineTree	(	CosineTree &	parentNode,
		const std::vector< size_t > &	subIndices
	)

CosineTree constructor for nodes other than the root node of the tree.

It takes in a pointer to the parent node and a list of column indices which mentions the columns to be included in the node. The function calculate the relevant variables just like the constructor above.

Parameters

parentNode	Pointer to the parent cosine node.
subIndices	Pointer to vector of column indices to be included.

mlpack::tree::CosineTree::CosineTree	(	const arma::mat &	dataset,
		const double	epsilon,
		const double	delta
	)

Construct the CosineTree and the basis for the given matrix, and passed 'epsilon' and 'delta' parameters.

The CosineTree is constructed by splitting nodes in the direction of maximum error, stored using a priority queue. Basis vectors are added from the left and right children of the split node. The basis vector from a node is the orthonormalized centroid of its columns. The splitting continues till the Monte Carlo estimate of the input matrix's projection on the obtained subspace is less than a fraction of the norm of the input matrix.

Parameters

dataset	Matrix for which the CosineTree is constructed.
epsilon	Error tolerance fraction for calculated subspace.
delta	Cumulative probability for Monte Carlo error lower bound.

mlpack::tree::CosineTree::~CosineTree ( )

Clean up the CosineTree: release allocated memory (including children).

Member Function Documentation

void mlpack::tree::CosineTree::BasisVector ( arma::vec & bVector )

inline

Set the basis vector of the node.

Definition at line 186 of file cosine_tree.hpp.

References basisVector.

arma::vec& mlpack::tree::CosineTree::BasisVector ( )

inline

Get the basis vector of the node.

Definition at line 189 of file cosine_tree.hpp.

References basisVector.

size_t mlpack::tree::CosineTree::BinarySearch	(	arma::vec &	cDistribution,
		double	value,
		size_t	start,
		size_t	end
	)

Sample a column based on the cumulative Length-Squared distribution of the cosine node, and a randomly generated value in the range [0, 1].

Binary search is more efficient than searching linearly for the same. This leads a significant speedup when there are large number of columns to choose from and when a number of samples are to be drawn from the distribution.

Parameters

cDistribution	Cumulative LS distribution of columns in the node.
value	Randomly generated value in the range [0, 1].
start	Starting index of the distribution interval to search in.
end	Ending index of the distribution interval to search in.

void mlpack::tree::CosineTree::CalculateCentroid ( )

Calculate centroid of the columns present in the node.

The calculated centroid is used as a basis vector for the cosine tree being constructed.

void mlpack::tree::CosineTree::CalculateCosines ( arma::vec & cosines )

Calculate cosines of the columns present in the node, with respect to the sampled splitting point.

The calculated cosine values are useful for splitting the node into its children.

Parameters

cosines Vector to store the cosine values in.

arma::vec& mlpack::tree::CosineTree::Centroid ( )

inline

Get pointer to the centroid vector.

Definition at line 183 of file cosine_tree.hpp.

References centroid.

size_t mlpack::tree::CosineTree::ColumnSampleLS ( )

Sample a point from the Length-Squared distribution of the cosine node.

The function uses 'l2NormsSquared' to calculate the cumulative probability distribution of the column vectors. The sampling is based on a randomly generated value in the range [0, 1].

void mlpack::tree::CosineTree::ColumnSamplesLS	(	std::vector< size_t > &	sampledIndices,
		arma::vec &	probabilities,
		size_t	numSamples
	)

Sample 'numSamples' points from the Length-Squared distribution of the cosine node.

The function uses 'l2NormsSquared' to calculate the cumulative probability distribution of the column vectors. The sampling is based on a randomly generated values in the range [0, 1].

void mlpack::tree::CosineTree::ConstructBasis ( CosineNodeQueue & treeQueue )

Constructs the final basis matrix, after the cosine tree construction.

Parameters

treeQueue Priority queue of cosine nodes.

void mlpack::tree::CosineTree::CosineNodeSplit ( )

This function splits the cosine node into two children based on the cosines of the columns contained in the node, with respect to the sampled splitting point.

The function also calls the CosineTree constructor for the children.

double mlpack::tree::CosineTree::FrobNormSquared ( ) const

inline

Get the Frobenius norm squared of columns in the node.

Definition at line 210 of file cosine_tree.hpp.

References frobNormSquared.

const arma::mat& mlpack::tree::CosineTree::GetDataset ( ) const

inline

Get pointer to the dataset matrix.

Definition at line 172 of file cosine_tree.hpp.

References dataset.

void mlpack::tree::CosineTree::GetFinalBasis ( arma::mat & finalBasis )

inline

Returns the basis of the constructed subspace.

Definition at line 169 of file cosine_tree.hpp.

References basis.

void mlpack::tree::CosineTree::L2Error ( const double error )

inline

Set the Monte Carlo error.

Definition at line 178 of file cosine_tree.hpp.

References l2Error.

Referenced by mlpack::tree::CompareCosineNode::operator()().

double mlpack::tree::CosineTree::L2Error ( ) const

inline

Get the Monte Carlo error.

Definition at line 180 of file cosine_tree.hpp.

References l2Error.

CosineTree* mlpack::tree::CosineTree::Left ( ) const

inline

Get pointer to the left child of the node.

Definition at line 197 of file cosine_tree.hpp.

References left.

CosineTree*& mlpack::tree::CosineTree::Left ( )

inline

Modify the pointer to the left child of the node.

Definition at line 199 of file cosine_tree.hpp.

References left.

void mlpack::tree::CosineTree::ModifiedGramSchmidt	(	CosineNodeQueue &	treeQueue,
		arma::vec &	centroid,
		arma::vec &	newBasisVector,
		arma::vec *	addBasisVector = `NULL`
	)

Calculates the orthonormalization of the passed centroid, with respect to the current vector subspace.

Parameters

treeQueue	Priority queue of cosine nodes.
centroid	Centroid of the node being added to the basis.
newBasisVector	Orthonormalized centroid of the node.
addBasisVector	Address to additional basis vector.

double mlpack::tree::CosineTree::MonteCarloError	(	CosineTree *	node,
		CosineNodeQueue &	treeQueue,
		arma::vec *	addBasisVector1 = `NULL`,
		arma::vec *	addBasisVector2 = `NULL`
	)

Estimates the squared error of the projection of the input node's matrix onto the current vector subspace.

A normal distribution is fit using weighted norms of projections of samples drawn from the input node's matrix columns. The error is calculated as the difference between the Frobenius norm of the input node's matrix and lower bound of the normal distribution.

Parameters

node	Node for which Monte Carlo estimate is calculated.
treeQueue	Priority queue of cosine nodes.
addBasisVector1	Address to first additional basis vector.
addBasisVector2	Address to second additional basis vector.

size_t mlpack::tree::CosineTree::NumColumns ( ) const

inline

Get number of columns of input matrix in the node.

Definition at line 207 of file cosine_tree.hpp.

References numColumns.

CosineTree* mlpack::tree::CosineTree::Parent ( ) const

inline

Get pointer to the parent node.

Definition at line 192 of file cosine_tree.hpp.

References parent.

CosineTree*& mlpack::tree::CosineTree::Parent ( )

inline

Modify the pointer to the parent node.

Definition at line 194 of file cosine_tree.hpp.

References parent.

CosineTree* mlpack::tree::CosineTree::Right ( ) const

inline

Get pointer to the right child of the node.

Definition at line 202 of file cosine_tree.hpp.

References right.

CosineTree*& mlpack::tree::CosineTree::Right ( )

inline

Modify the pointer to the left child of the node.

Definition at line 204 of file cosine_tree.hpp.

References right.

size_t mlpack::tree::CosineTree::SplitPointIndex ( ) const

inline

Get the column index of split point of the node.

Definition at line 213 of file cosine_tree.hpp.

References indices, and splitPointIndex.

std::vector<size_t>& mlpack::tree::CosineTree::VectorIndices ( )

inline

Get the indices of columns in the node.

Definition at line 175 of file cosine_tree.hpp.

References indices.

Member Data Documentation

arma::mat mlpack::tree::CosineTree::basis

private

Subspace basis of the input dataset.

Definition at line 221 of file cosine_tree.hpp.

Referenced by GetFinalBasis().

arma::vec mlpack::tree::CosineTree::basisVector

private

Orthonormalized basis vector of the node.

Definition at line 235 of file cosine_tree.hpp.

Referenced by BasisVector().

arma::vec mlpack::tree::CosineTree::centroid

private

Centroid of columns of input matrix in the node.

Definition at line 233 of file cosine_tree.hpp.

Referenced by Centroid().

const arma::mat& mlpack::tree::CosineTree::dataset

private

Matrix for which cosine tree is constructed.

Definition at line 217 of file cosine_tree.hpp.

Referenced by GetDataset().

double mlpack::tree::CosineTree::delta

private

Cumulative probability for Monte Carlo error lower bound.

Definition at line 219 of file cosine_tree.hpp.

double mlpack::tree::CosineTree::frobNormSquared

private

Frobenius norm squared of columns in the node.

Definition at line 243 of file cosine_tree.hpp.

Referenced by FrobNormSquared().

std::vector<size_t> mlpack::tree::CosineTree::indices

private

Indices of columns of input matrix in the node.

Definition at line 229 of file cosine_tree.hpp.

Referenced by SplitPointIndex(), and VectorIndices().

double mlpack::tree::CosineTree::l2Error

private

Monte Carlo error for this node.

Definition at line 241 of file cosine_tree.hpp.

Referenced by L2Error().

arma::vec mlpack::tree::CosineTree::l2NormsSquared

private

L2-norm squared of columns in the node.

Definition at line 231 of file cosine_tree.hpp.

CosineTree* mlpack::tree::CosineTree::left

private

Left child of the node.

Definition at line 225 of file cosine_tree.hpp.

Referenced by Left().

size_t mlpack::tree::CosineTree::numColumns

private

Number of columns of input matrix in the node.

Definition at line 239 of file cosine_tree.hpp.

Referenced by NumColumns().

CosineTree* mlpack::tree::CosineTree::parent

private

Parent of the node.

Definition at line 223 of file cosine_tree.hpp.

Referenced by Parent().

CosineTree* mlpack::tree::CosineTree::right

private

Right child of the node.

Definition at line 227 of file cosine_tree.hpp.

Referenced by Right().

size_t mlpack::tree::CosineTree::splitPointIndex

private

Index of split point of cosine node.

Definition at line 237 of file cosine_tree.hpp.

Referenced by SplitPointIndex().

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

src/mlpack/core/tree/cosine_tree/cosine_tree.hpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation