.TH "mlpack::tree::CosineTree" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::tree::CosineTree \- 
.SH SYNOPSIS
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.PP
.SS "Public Member Functions"

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.RI "\fBCosineTree\fP (const arma::mat &\fBdataset\fP)"
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.RI "\fI\fBCosineTree\fP constructor for the root node of the tree\&. \fP"
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.RI "\fBCosineTree\fP (\fBCosineTree\fP &parentNode, const std::vector< size_t > &subIndices)"
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.RI "\fI\fBCosineTree\fP constructor for nodes other than the root node of the tree\&. \fP"
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.RI "\fBCosineTree\fP (const arma::mat &\fBdataset\fP, const double \fBepsilon\fP, const double \fBdelta\fP)"
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.RI "\fIConstruct the \fBCosineTree\fP and the basis for the given matrix, and passed 'epsilon' and 'delta' parameters\&. \fP"
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.RI "void \fBBasisVector\fP (arma::vec &bVector)"
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.RI "\fISet the basis vector of the node\&. \fP"
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.RI "arma::vec & \fBBasisVector\fP ()"
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.RI "\fIGet the basis vector of the node\&. \fP"
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.RI "size_t \fBBinarySearch\fP (arma::vec &cDistribution, double value, size_t start, size_t end)"
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.RI "\fISample a column based on the cumulative Length-Squared distribution of the cosine node, and a randomly generated value in the range [0, 1]\&. \fP"
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.RI "void \fBCalculateCentroid\fP ()"
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.RI "\fICalculate centroid of the columns present in the node\&. \fP"
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.RI "void \fBCalculateCosines\fP (arma::vec &cosines)"
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.RI "\fICalculate cosines of the columns present in the node, with respect to the sampled splitting point\&. \fP"
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.RI "arma::vec & \fBCentroid\fP ()"
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.RI "\fIGet pointer to the centroid vector\&. \fP"
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.RI "size_t \fBColumnSampleLS\fP ()"
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.RI "\fISample a point from the Length-Squared distribution of the cosine node\&. \fP"
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.RI "void \fBColumnSamplesLS\fP (std::vector< size_t > &sampledIndices, arma::vec &probabilities, size_t numSamples)"
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.RI "\fISample 'numSamples' points from the Length-Squared distribution of the cosine node\&. \fP"
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.RI "void \fBConstructBasis\fP (\fBCosineNodeQueue\fP &treeQueue)"
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.RI "\fIConstructs the final basis matrix, after the cosine tree construction\&. \fP"
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.RI "void \fBCosineNodeSplit\fP ()"
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.RI "\fIThis 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\&. \fP"
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.RI "double \fBFrobNormSquared\fP () const "
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.RI "\fIGet the Frobenius norm squared of columns in the node\&. \fP"
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.RI "const arma::mat & \fBGetDataset\fP () const "
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.RI "\fIGet pointer to the dataset matrix\&. \fP"
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.RI "void \fBGetFinalBasis\fP (arma::mat &finalBasis)"
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.RI "\fIReturns the basis of the constructed subspace\&. \fP"
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.RI "void \fBL2Error\fP (const double error)"
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.RI "\fISet the Monte Carlo error\&. \fP"
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.RI "double \fBL2Error\fP () const "
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.RI "\fIGet the Monte Carlo error\&. \fP"
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.RI "\fBCosineTree\fP * \fBLeft\fP ()"
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.RI "\fIGet pointer to the left child of the node\&. \fP"
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.RI "void \fBModifiedGramSchmidt\fP (\fBCosineNodeQueue\fP &treeQueue, arma::vec &\fBcentroid\fP, arma::vec &newBasisVector, arma::vec *addBasisVector=NULL)"
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.RI "\fICalculates the orthonormalization of the passed centroid, with respect to the current vector subspace\&. \fP"
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.RI "double \fBMonteCarloError\fP (\fBCosineTree\fP *node, \fBCosineNodeQueue\fP &treeQueue, arma::vec *addBasisVector1=NULL, arma::vec *addBasisVector2=NULL)"
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.RI "\fIEstimates the squared error of the projection of the input node's matrix onto the current vector subspace\&. \fP"
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.RI "size_t \fBNumColumns\fP () const "
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.RI "\fIGet number of columns of input matrix in the node\&. \fP"
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.RI "\fBCosineTree\fP * \fBRight\fP ()"
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.RI "\fIGet pointer to the right child of the node\&. \fP"
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.RI "size_t \fBSplitPointIndex\fP () const "
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.RI "\fIGet the column index of split point of the node\&. \fP"
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.RI "std::vector< size_t > & \fBVectorIndices\fP ()"
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.RI "\fIGet the indices of columns in the node\&. \fP"
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.SS "Private Attributes"

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.RI "arma::mat \fBbasis\fP"
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.RI "\fISubspace basis of the input dataset\&. \fP"
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.RI "arma::vec \fBbasisVector\fP"
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.RI "\fIOrthonormalized basis vector of the node\&. \fP"
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.RI "arma::vec \fBcentroid\fP"
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.RI "\fICentroid of columns of input matrix in the node\&. \fP"
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.RI "const arma::mat & \fBdataset\fP"
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.RI "\fIMatrix for which cosine tree is constructed\&. \fP"
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.RI "double \fBdelta\fP"
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.RI "\fICumulative probability for Monte Carlo error lower bound\&. \fP"
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.RI "double \fBepsilon\fP"
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.RI "\fIError tolerance fraction for calculated subspace\&. \fP"
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.RI "double \fBfrobNormSquared\fP"
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.RI "\fIFrobenius norm squared of columns in the node\&. \fP"
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.RI "std::vector< size_t > \fBindices\fP"
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.RI "\fIIndices of columns of input matrix in the node\&. \fP"
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.RI "double \fBl2Error\fP"
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.RI "\fIMonte Carlo error for this node\&. \fP"
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.RI "arma::vec \fBl2NormsSquared\fP"
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.RI "\fIL2-norm squared of columns in the node\&. \fP"
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.RI "\fBCosineTree\fP * \fBleft\fP"
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.RI "\fILeft child of the node\&. \fP"
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.RI "size_t \fBnumColumns\fP"
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.RI "\fINumber of columns of input matrix in the node\&. \fP"
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.RI "\fBCosineTree\fP * \fBparent\fP"
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.RI "\fIParent of the node\&. \fP"
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.RI "\fBCosineTree\fP * \fBright\fP"
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.RI "\fIRight child of the node\&. \fP"
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.RI "size_t \fBsplitPointIndex\fP"
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.RI "\fIIndex of split point of cosine node\&. \fP"
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.SH "Detailed Description"
.PP 
Definition at line 40 of file cosine_tree\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "mlpack::tree::CosineTree::CosineTree (const arma::mat &dataset)"

.PP
\fBCosineTree\fP 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\&.
.PP
\fBParameters:\fP
.RS 4
\fIdataset\fP Matrix for which cosine tree is constructed\&. 
.RE
.PP

.SS "mlpack::tree::CosineTree::CosineTree (\fBCosineTree\fP &parentNode, const std::vector< size_t > &subIndices)"

.PP
\fBCosineTree\fP 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\&.
.PP
\fBParameters:\fP
.RS 4
\fIparentNode\fP Pointer to the parent cosine node\&. 
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\fIsubIndices\fP Pointer to vector of column indices to be included\&. 
.RE
.PP

.SS "mlpack::tree::CosineTree::CosineTree (const arma::mat &dataset, const doubleepsilon, const doubledelta)"

.PP
Construct the \fBCosineTree\fP and the basis for the given matrix, and passed 'epsilon' and 'delta' parameters\&. The \fBCosineTree\fP 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\&.
.PP
\fBParameters:\fP
.RS 4
\fIdataset\fP Matrix for which the \fBCosineTree\fP is constructed\&. 
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\fIepsilon\fP Error tolerance fraction for calculated subspace\&. 
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\fIdelta\fP Cumulative probability for Monte Carlo error lower bound\&. 
.RE
.PP

.SH "Member Function Documentation"
.PP 
.SS "void mlpack::tree::CosineTree::BasisVector (arma::vec &bVector)\fC [inline]\fP"

.PP
Set the basis vector of the node\&. 
.PP
Definition at line 194 of file cosine_tree\&.hpp\&.
.PP
References basisVector\&.
.SS "arma::vec& mlpack::tree::CosineTree::BasisVector ()\fC [inline]\fP"

.PP
Get the basis vector of the node\&. 
.PP
Definition at line 197 of file cosine_tree\&.hpp\&.
.PP
References basisVector\&.
.SS "size_t mlpack::tree::CosineTree::BinarySearch (arma::vec &cDistribution, doublevalue, size_tstart, size_tend)"

.PP
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\&.
.PP
\fBParameters:\fP
.RS 4
\fIcDistribution\fP Cumulative LS distibution of columns in the node\&. 
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\fIvalue\fP Randomly generated value in the range [0, 1]\&. 
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\fIstart\fP Starting index of the distribution interval to search in\&. 
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\fIend\fP Ending index of the distribution interval to search in\&. 
.RE
.PP

.SS "void mlpack::tree::CosineTree::CalculateCentroid ()"

.PP
Calculate centroid of the columns present in the node\&. The calculated centroid is used as a basis vector for the cosine tree being constructed\&. 
.SS "void mlpack::tree::CosineTree::CalculateCosines (arma::vec &cosines)"

.PP
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\&.
.PP
\fBParameters:\fP
.RS 4
\fIcosines\fP Vector to store the cosine values in\&. 
.RE
.PP

.SS "arma::vec& mlpack::tree::CosineTree::Centroid ()\fC [inline]\fP"

.PP
Get pointer to the centroid vector\&. 
.PP
Definition at line 191 of file cosine_tree\&.hpp\&.
.PP
References centroid\&.
.SS "size_t mlpack::tree::CosineTree::ColumnSampleLS ()"

.PP
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]\&. 
.SS "void mlpack::tree::CosineTree::ColumnSamplesLS (std::vector< size_t > &sampledIndices, arma::vec &probabilities, size_tnumSamples)"

.PP
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]\&. 
.SS "void mlpack::tree::CosineTree::ConstructBasis (\fBCosineNodeQueue\fP &treeQueue)"

.PP
Constructs the final basis matrix, after the cosine tree construction\&. 
.PP
\fBParameters:\fP
.RS 4
\fItreeQueue\fP Priority queue of cosine nodes\&. 
.RE
.PP

.SS "void mlpack::tree::CosineTree::CosineNodeSplit ()"

.PP
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 \fBCosineTree\fP constructor for the children\&. 
.SS "double mlpack::tree::CosineTree::FrobNormSquared () const\fC [inline]\fP"

.PP
Get the Frobenius norm squared of columns in the node\&. 
.PP
Definition at line 209 of file cosine_tree\&.hpp\&.
.PP
References frobNormSquared\&.
.SS "const arma::mat& mlpack::tree::CosineTree::GetDataset () const\fC [inline]\fP"

.PP
Get pointer to the dataset matrix\&. 
.PP
Definition at line 179 of file cosine_tree\&.hpp\&.
.PP
References dataset\&.
.SS "void mlpack::tree::CosineTree::GetFinalBasis (arma::mat &finalBasis)\fC [inline]\fP"

.PP
Returns the basis of the constructed subspace\&. 
.PP
Definition at line 176 of file cosine_tree\&.hpp\&.
.PP
References basis\&.
.SS "void mlpack::tree::CosineTree::L2Error (const doubleerror)\fC [inline]\fP"

.PP
Set the Monte Carlo error\&. 
.PP
Definition at line 185 of file cosine_tree\&.hpp\&.
.PP
References l2Error\&.
.PP
Referenced by mlpack::tree::CompareCosineNode::operator()()\&.
.SS "double mlpack::tree::CosineTree::L2Error () const\fC [inline]\fP"

.PP
Get the Monte Carlo error\&. 
.PP
Definition at line 188 of file cosine_tree\&.hpp\&.
.PP
References l2Error\&.
.SS "\fBCosineTree\fP* mlpack::tree::CosineTree::Left ()\fC [inline]\fP"

.PP
Get pointer to the left child of the node\&. 
.PP
Definition at line 200 of file cosine_tree\&.hpp\&.
.PP
References left\&.
.SS "void mlpack::tree::CosineTree::ModifiedGramSchmidt (\fBCosineNodeQueue\fP &treeQueue, arma::vec &centroid, arma::vec &newBasisVector, arma::vec *addBasisVector = \fCNULL\fP)"

.PP
Calculates the orthonormalization of the passed centroid, with respect to the current vector subspace\&. 
.PP
\fBParameters:\fP
.RS 4
\fItreeQueue\fP Priority queue of cosine nodes\&. 
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\fIcentroid\fP Centroid of the node being added to the basis\&. 
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\fInewBasisVector\fP Orthonormalized centroid of the node\&. 
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\fIaddBasisVector\fP Address to additional basis vector\&. 
.RE
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.SS "double mlpack::tree::CosineTree::MonteCarloError (\fBCosineTree\fP *node, \fBCosineNodeQueue\fP &treeQueue, arma::vec *addBasisVector1 = \fCNULL\fP, arma::vec *addBasisVector2 = \fCNULL\fP)"

.PP
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\&.
.PP
\fBParameters:\fP
.RS 4
\fInode\fP Node for which Monte Carlo estimate is calculated\&. 
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\fItreeQueue\fP Priority queue of cosine nodes\&. 
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\fIaddBasisVector1\fP Address to first additional basis vector\&. 
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\fIaddBasisVector2\fP Address to second additional basis vector\&. 
.RE
.PP

.SS "size_t mlpack::tree::CosineTree::NumColumns () const\fC [inline]\fP"

.PP
Get number of columns of input matrix in the node\&. 
.PP
Definition at line 206 of file cosine_tree\&.hpp\&.
.PP
References numColumns\&.
.SS "\fBCosineTree\fP* mlpack::tree::CosineTree::Right ()\fC [inline]\fP"

.PP
Get pointer to the right child of the node\&. 
.PP
Definition at line 203 of file cosine_tree\&.hpp\&.
.PP
References right\&.
.SS "size_t mlpack::tree::CosineTree::SplitPointIndex () const\fC [inline]\fP"

.PP
Get the column index of split point of the node\&. 
.PP
Definition at line 212 of file cosine_tree\&.hpp\&.
.PP
References indices, and splitPointIndex\&.
.SS "std::vector<size_t>& mlpack::tree::CosineTree::VectorIndices ()\fC [inline]\fP"

.PP
Get the indices of columns in the node\&. 
.PP
Definition at line 182 of file cosine_tree\&.hpp\&.
.PP
References indices\&.
.SH "Member Data Documentation"
.PP 
.SS "arma::mat mlpack::tree::CosineTree::basis\fC [private]\fP"

.PP
Subspace basis of the input dataset\&. 
.PP
Definition at line 222 of file cosine_tree\&.hpp\&.
.PP
Referenced by GetFinalBasis()\&.
.SS "arma::vec mlpack::tree::CosineTree::basisVector\fC [private]\fP"

.PP
Orthonormalized basis vector of the node\&. 
.PP
Definition at line 236 of file cosine_tree\&.hpp\&.
.PP
Referenced by BasisVector()\&.
.SS "arma::vec mlpack::tree::CosineTree::centroid\fC [private]\fP"

.PP
Centroid of columns of input matrix in the node\&. 
.PP
Definition at line 234 of file cosine_tree\&.hpp\&.
.PP
Referenced by Centroid()\&.
.SS "const arma::mat& mlpack::tree::CosineTree::dataset\fC [private]\fP"

.PP
Matrix for which cosine tree is constructed\&. 
.PP
Definition at line 216 of file cosine_tree\&.hpp\&.
.PP
Referenced by GetDataset()\&.
.SS "double mlpack::tree::CosineTree::delta\fC [private]\fP"

.PP
Cumulative probability for Monte Carlo error lower bound\&. 
.PP
Definition at line 220 of file cosine_tree\&.hpp\&.
.SS "double mlpack::tree::CosineTree::epsilon\fC [private]\fP"

.PP
Error tolerance fraction for calculated subspace\&. 
.PP
Definition at line 218 of file cosine_tree\&.hpp\&.
.SS "double mlpack::tree::CosineTree::frobNormSquared\fC [private]\fP"

.PP
Frobenius norm squared of columns in the node\&. 
.PP
Definition at line 244 of file cosine_tree\&.hpp\&.
.PP
Referenced by FrobNormSquared()\&.
.SS "std::vector<size_t> mlpack::tree::CosineTree::indices\fC [private]\fP"

.PP
Indices of columns of input matrix in the node\&. 
.PP
Definition at line 230 of file cosine_tree\&.hpp\&.
.PP
Referenced by SplitPointIndex(), and VectorIndices()\&.
.SS "double mlpack::tree::CosineTree::l2Error\fC [private]\fP"

.PP
Monte Carlo error for this node\&. 
.PP
Definition at line 242 of file cosine_tree\&.hpp\&.
.PP
Referenced by L2Error()\&.
.SS "arma::vec mlpack::tree::CosineTree::l2NormsSquared\fC [private]\fP"

.PP
L2-norm squared of columns in the node\&. 
.PP
Definition at line 232 of file cosine_tree\&.hpp\&.
.SS "\fBCosineTree\fP* mlpack::tree::CosineTree::left\fC [private]\fP"

.PP
Left child of the node\&. 
.PP
Definition at line 228 of file cosine_tree\&.hpp\&.
.PP
Referenced by Left()\&.
.SS "size_t mlpack::tree::CosineTree::numColumns\fC [private]\fP"

.PP
Number of columns of input matrix in the node\&. 
.PP
Definition at line 240 of file cosine_tree\&.hpp\&.
.PP
Referenced by NumColumns()\&.
.SS "\fBCosineTree\fP* mlpack::tree::CosineTree::parent\fC [private]\fP"

.PP
Parent of the node\&. 
.PP
Definition at line 224 of file cosine_tree\&.hpp\&.
.SS "\fBCosineTree\fP* mlpack::tree::CosineTree::right\fC [private]\fP"

.PP
Right child of the node\&. 
.PP
Definition at line 226 of file cosine_tree\&.hpp\&.
.PP
Referenced by Right()\&.
.SS "size_t mlpack::tree::CosineTree::splitPointIndex\fC [private]\fP"

.PP
Index of split point of cosine node\&. 
.PP
Definition at line 238 of file cosine_tree\&.hpp\&.
.PP
Referenced by SplitPointIndex()\&.

.SH "Author"
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