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 (const CosineTree &other)
	Copy the given tree. More...

	CosineTree (CosineTree &&other)
	Move the given tree. More...

CosineTree &	operator= (const CosineTree &other)
	Copy the given Cosine Tree. More...

CosineTree &	operator= (CosineTree &&other)
	Take ownership of the given Cosine Tree. More...

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

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...

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...

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...

size_t	ColumnSampleLS ()
	Sample a point from the Length-Squared distribution of the cosine 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	CalculateCosines (arma::vec &cosines)
	Calculate cosines of the columns present in the node, with respect to the sampled splitting point. More...

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

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

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

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

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

double	L2Error () const
	Get the Monte Carlo error.

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

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

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

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

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

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

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

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

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

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

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

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

Constructor & Destructor Documentation

◆ CosineTree() [1/5]

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.

◆ CosineTree() [2/5]

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.

◆ CosineTree() [3/5]

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.

◆ CosineTree() [4/5]

mlpack::tree::CosineTree::CosineTree ( const CosineTree & other )

Copy the given tree.

Be careful! This may use a lot of memory.

Parameters

other Tree to copy from.

◆ CosineTree() [5/5]

mlpack::tree::CosineTree::CosineTree ( CosineTree && other )

Move the given tree.

The tree passed as a parameter will be emptied and will not be usable after this call.

Parameters

other Tree to move.

Member Function Documentation

◆ BinarySearch()

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.

◆ CalculateCentroid()

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.

◆ CalculateCosines()

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.

◆ ColumnSampleLS()

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].

◆ ColumnSamplesLS()

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].

◆ ConstructBasis()

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

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

Parameters

treeQueue Priority queue of cosine nodes.

◆ CosineNodeSplit()

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.

◆ ModifiedGramSchmidt()

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.

◆ MonteCarloError()

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.

◆ operator=() [1/2]

CosineTree & mlpack::tree::CosineTree::operator= ( const CosineTree & other )

Copy the given Cosine Tree.

Copy assignment operator: copy the given other tree.

Parameters

other The tree to be copied.

◆ operator=() [2/2]

CosineTree & mlpack::tree::CosineTree::operator= ( CosineTree && other )

Take ownership of the given Cosine Tree.

Move assignment operator: take ownership of the given tree.

Parameters

other The tree to take ownership of.

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

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

Public Member Functions

Constructor & Destructor Documentation

◆ CosineTree() [1/5]

◆ CosineTree() [2/5]

◆ CosineTree() [3/5]

◆ CosineTree() [4/5]

◆ CosineTree() [5/5]

Member Function Documentation

◆ BinarySearch()

◆ CalculateCentroid()

◆ CalculateCosines()

◆ ColumnSampleLS()

◆ ColumnSamplesLS()

◆ ConstructBasis()

◆ CosineNodeSplit()

◆ ModifiedGramSchmidt()

◆ MonteCarloError()

◆ operator=() [1/2]

◆ operator=() [2/2]