mlpack_tree_CosineTree (3)

Public Member Functions

CosineTree (const arma::mat &dataset)

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

CosineTree constructor for nodes other than the root node of the tree. 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. void BasisVector (arma::vec &bVector)

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

Get the basis vector of the node. 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]. void CalculateCentroid ()

Calculate centroid of the columns present in the node. void CalculateCosines (arma::vec &cosines)

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

Get pointer to the centroid vector. size_t ColumnSampleLS ()

Sample a point from the Length-Squared distribution of the cosine node. 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. void ConstructBasis (CosineNodeQueue &treeQueue)

Constructs the final basis matrix, after the cosine tree construction. 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. double FrobNormSquared () const

Get the Frobenius norm squared of columns in the node. const arma::mat & GetDataset () const

Get pointer to the dataset matrix. void GetFinalBasis (arma::mat &finalBasis)

Returns the basis of the constructed subspace. void L2Error (const double error)

Set the Monte Carlo error. double L2Error () const

Get the Monte Carlo error. CosineTree * Left ()

Get pointer to the left child of the node. 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. 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. size_t NumColumns () const

Get number of columns of input matrix in the node. CosineTree * Right ()

Get pointer to the right child of the node. size_t SplitPointIndex () const

Get the column index of split point of the node. std::vector< size_t > & VectorIndices ()

Get the indices of columns in the node.

Private Attributes

arma::mat basis

Subspace basis of the input dataset. arma::vec basisVector

Orthonormalized basis vector of the node. arma::vec centroid

Centroid of columns of input matrix in the node. const arma::mat & dataset

Matrix for which cosine tree is constructed. double delta

Cumulative probability for Monte Carlo error lower bound. double epsilon

Error tolerance fraction for calculated subspace. double frobNormSquared

Frobenius norm squared of columns in the node. std::vector< size_t > indices

Indices of columns of input matrix in the node. double l2Error

Monte Carlo error for this node. arma::vec l2NormsSquared

L2-norm squared of columns in the node. CosineTree * left

Left child of the node. size_t numColumns

Number of columns of input matrix in the node. CosineTree * parent

Parent of the node. CosineTree * right

Right child of the node. size_t splitPointIndex

Index of split point of cosine node.

Definition at line 40 of file cosine_tree.hpp.

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 (\fBCosineTree\fP &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 doubleepsilon, const doubledelta)

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.

void mlpack::tree::CosineTree::BasisVector (arma::vec &bVector)\fC [inline]\fP

Set the basis vector of the node.

Definition at line 194 of file cosine_tree.hpp.

References basisVector.

arma::vec& mlpack::tree::CosineTree::BasisVector ()\fC [inline]\fP

Get the basis vector of the node.

Definition at line 197 of file cosine_tree.hpp.

References basisVector.

size_t mlpack::tree::CosineTree::BinarySearch (arma::vec &cDistribution, doublevalue, size_tstart, size_tend)

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 distibution 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 ()\fC [inline]\fP

Get pointer to the centroid vector.

Definition at line 191 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_tnumSamples)

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 (\fBCosineNodeQueue\fP &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\fC [inline]\fP

Get the Frobenius norm squared of columns in the node.

Definition at line 209 of file cosine_tree.hpp.

References frobNormSquared.

const arma::mat& mlpack::tree::CosineTree::GetDataset () const\fC [inline]\fP

Get pointer to the dataset matrix.

Definition at line 179 of file cosine_tree.hpp.

References dataset.

void mlpack::tree::CosineTree::GetFinalBasis (arma::mat &finalBasis)\fC [inline]\fP

Returns the basis of the constructed subspace.

Definition at line 176 of file cosine_tree.hpp.

References basis.

void mlpack::tree::CosineTree::L2Error (const doubleerror)\fC [inline]\fP

Set the Monte Carlo error.

Definition at line 185 of file cosine_tree.hpp.

References l2Error.

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

double mlpack::tree::CosineTree::L2Error () const\fC [inline]\fP

Get the Monte Carlo error.

Definition at line 188 of file cosine_tree.hpp.

References l2Error.

\fBCosineTree\fP* mlpack::tree::CosineTree::Left ()\fC [inline]\fP

Get pointer to the left child of the node.

Definition at line 200 of file cosine_tree.hpp.

References left.

void mlpack::tree::CosineTree::ModifiedGramSchmidt (\fBCosineNodeQueue\fP &treeQueue, arma::vec ¢roid, arma::vec &newBasisVector, arma::vec *addBasisVector = \fCNULL\fP)

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 (\fBCosineTree\fP *node, \fBCosineNodeQueue\fP &treeQueue, arma::vec *addBasisVector1 = \fCNULL\fP, arma::vec *addBasisVector2 = \fCNULL\fP)

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\fC [inline]\fP

Get number of columns of input matrix in the node.

Definition at line 206 of file cosine_tree.hpp.

References numColumns.

\fBCosineTree\fP* mlpack::tree::CosineTree::Right ()\fC [inline]\fP

Get pointer to the right child of the node.

Definition at line 203 of file cosine_tree.hpp.

References right.

size_t mlpack::tree::CosineTree::SplitPointIndex () const\fC [inline]\fP

Get the column index of split point of the node.

Definition at line 212 of file cosine_tree.hpp.

References indices, and splitPointIndex.

std::vector<size_t>& mlpack::tree::CosineTree::VectorIndices ()\fC [inline]\fP

Get the indices of columns in the node.

Definition at line 182 of file cosine_tree.hpp.

References indices.

arma::mat mlpack::tree::CosineTree::basis\fC [private]\fP

Subspace basis of the input dataset.

Definition at line 222 of file cosine_tree.hpp.

Referenced by GetFinalBasis().

arma::vec mlpack::tree::CosineTree::basisVector\fC [private]\fP

Orthonormalized basis vector of the node.

Definition at line 236 of file cosine_tree.hpp.

Referenced by BasisVector().

arma::vec mlpack::tree::CosineTree::centroid\fC [private]\fP

Centroid of columns of input matrix in the node.

Definition at line 234 of file cosine_tree.hpp.

Referenced by Centroid().

const arma::mat& mlpack::tree::CosineTree::dataset\fC [private]\fP

Matrix for which cosine tree is constructed.

Definition at line 216 of file cosine_tree.hpp.

Referenced by GetDataset().

double mlpack::tree::CosineTree::delta\fC [private]\fP

Cumulative probability for Monte Carlo error lower bound.

Definition at line 220 of file cosine_tree.hpp.

double mlpack::tree::CosineTree::epsilon\fC [private]\fP

Error tolerance fraction for calculated subspace.

Definition at line 218 of file cosine_tree.hpp.

double mlpack::tree::CosineTree::frobNormSquared\fC [private]\fP

Frobenius norm squared of columns in the node.

Definition at line 244 of file cosine_tree.hpp.

Referenced by FrobNormSquared().

std::vector<size_t> mlpack::tree::CosineTree::indices\fC [private]\fP

Indices of columns of input matrix in the node.

Definition at line 230 of file cosine_tree.hpp.

Referenced by SplitPointIndex(), and VectorIndices().

double mlpack::tree::CosineTree::l2Error\fC [private]\fP

Monte Carlo error for this node.

Definition at line 242 of file cosine_tree.hpp.

Referenced by L2Error().

arma::vec mlpack::tree::CosineTree::l2NormsSquared\fC [private]\fP

L2-norm squared of columns in the node.

Definition at line 232 of file cosine_tree.hpp.

\fBCosineTree\fP* mlpack::tree::CosineTree::left\fC [private]\fP

Left child of the node.

Definition at line 228 of file cosine_tree.hpp.

Referenced by Left().

size_t mlpack::tree::CosineTree::numColumns\fC [private]\fP

Number of columns of input matrix in the node.

Definition at line 240 of file cosine_tree.hpp.

Referenced by NumColumns().

\fBCosineTree\fP* mlpack::tree::CosineTree::parent\fC [private]\fP

Parent of the node.

Definition at line 224 of file cosine_tree.hpp.

\fBCosineTree\fP* mlpack::tree::CosineTree::right\fC [private]\fP

Right child of the node.

Definition at line 226 of file cosine_tree.hpp.

Referenced by Right().

size_t mlpack::tree::CosineTree::splitPointIndex\fC [private]\fP

Index of split point of cosine node.

Definition at line 238 of file cosine_tree.hpp.

Referenced by SplitPointIndex().

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