.TH "mlpack::kpca::KernelPCA< KernelType, KernelRule >" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::kpca::KernelPCA< KernelType, KernelRule > \- 
.PP
This class performs kernel principal components analysis (Kernel PCA), for a given kernel\&.  

.SH SYNOPSIS
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.PP
.SS "Public Member Functions"

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.RI "\fBKernelPCA\fP (const KernelType \fBkernel\fP=KernelType(), const bool \fBcenterTransformedData\fP=false)"
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.RI "\fIConstruct the \fBKernelPCA\fP object, optionally passing a kernel\&. \fP"
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.RI "void \fBApply\fP (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec, const size_t newDimension)"
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.RI "\fIApply Kernel Principal Components Analysis to the provided data set\&. \fP"
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.RI "void \fBApply\fP (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec)"
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.RI "\fIApply Kernel Principal Components Analysis to the provided data set\&. \fP"
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.RI "void \fBApply\fP (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval)"
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.RI "\fIApply Kernel Principal Component Analysis to the provided data set\&. \fP"
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.RI "void \fBApply\fP (arma::mat &data, const size_t newDimension)"
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.RI "\fIApply dimensionality reduction using Kernel Principal Component Analysis to the provided data set\&. \fP"
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.RI "bool \fBCenterTransformedData\fP () const "
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.RI "\fIReturn whether or not the transformed data is centered\&. \fP"
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.RI "bool & \fBCenterTransformedData\fP ()"
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.RI "\fIReturn whether or not the transformed data is centered\&. \fP"
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.RI "const KernelType & \fBKernel\fP () const "
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.RI "\fIGet the kernel\&. \fP"
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.RI "KernelType & \fBKernel\fP ()"
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.RI "\fIModify the kernel\&. \fP"
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.RI "std::string \fBToString\fP () const "
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.SS "Private Attributes"

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.RI "bool \fBcenterTransformedData\fP"
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.RI "\fIIf true, the data will be scaled (by standard deviation) when \fBApply()\fP is run\&. \fP"
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.RI "KernelType \fBkernel\fP"
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.RI "\fIThe instantiated kernel\&. \fP"
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.SH "Detailed Description"
.PP 

.SS "template<typename KernelType, typename KernelRule = NaiveKernelRule<KernelType>>class mlpack::kpca::KernelPCA< KernelType, KernelRule >"
This class performs kernel principal components analysis (Kernel PCA), for a given kernel\&. 

This is a standard machine learning technique and is well-documented on the Internet and in standard texts\&. It is often used as a dimensionality reduction technique, and can also be useful in mapping linearly inseparable classes of points to different spaces where they are linearly separable\&.
.PP
The performance of the method is highly dependent on the kernel choice\&. There are numerous available kernels in the \fBmlpack::kernel\fP namespace (see files in mlpack/core/kernels/) and it is easy to write your own; see other implementations for examples\&. 
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Definition at line 50 of file kernel_pca\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::\fBKernelPCA\fP (const KernelTypekernel = \fCKernelType()\fP, const boolcenterTransformedData = \fCfalse\fP)"

.PP
Construct the \fBKernelPCA\fP object, optionally passing a kernel\&. Optionally, the transformed data can be centered about the origin; to do this, pass 'true' for centerTransformedData\&. This will take slightly longer (but not much)\&.
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\fBParameters:\fP
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\fIkernel\fP Kernel to be used for computation\&. 
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\fIcenterTransformedData\fP Center transformed data\&. 
.RE
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.SH "Member Function Documentation"
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.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> void \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec, const size_tnewDimension)"

.PP
Apply Kernel Principal Components Analysis to the provided data set\&. 
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\fBParameters:\fP
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\fIdata\fP Data matrix\&. 
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\fItransformedData\fP Matrix to output results into\&. 
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\fIeigval\fP KPCA eigenvalues will be written to this vector\&. 
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\fIeigvec\fP KPCA eigenvectors will be written to this matrix\&. 
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\fInewDimension\fP New dimension for the dataset\&. 
.RE
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.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> void \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec)"

.PP
Apply Kernel Principal Components Analysis to the provided data set\&. 
.PP
\fBParameters:\fP
.RS 4
\fIdata\fP Data matrix\&. 
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\fItransformedData\fP Matrix to output results into\&. 
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\fIeigval\fP KPCA eigenvalues will be written to this vector\&. 
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\fIeigvec\fP KPCA eigenvectors will be written to this matrix\&. 
.RE
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.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> void \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval)"

.PP
Apply Kernel Principal Component Analysis to the provided data set\&. 
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\fBParameters:\fP
.RS 4
\fIdata\fP Data matrix\&. 
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\fItransformedData\fP Matrix to output results into\&. 
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\fIeigval\fP KPCA eigenvalues will be written to this vector\&. 
.RE
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.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> void \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Apply (arma::mat &data, const size_tnewDimension)"

.PP
Apply dimensionality reduction using Kernel Principal Component Analysis to the provided data set\&. The data matrix will be modified in-place\&. Note that the dimension can be larger than the existing dimension because KPCA works on the kernel matrix, not the covariance matrix\&. This means the new dimension can be as large as the number of points (columns) in the dataset\&. Note that if you specify newDimension to be larger than the current dimension of the data (the number of rows), then it's not really 'dimensionality reduction'\&.\&.\&.
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\fBParameters:\fP
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\fIdata\fP Data matrix\&. 
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\fInewDimension\fP New dimension for the dataset\&. 
.RE
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.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> bool \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::CenterTransformedData () const\fC [inline]\fP"

.PP
Return whether or not the transformed data is centered\&. 
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Definition at line 125 of file kernel_pca\&.hpp\&.
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References mlpack::kpca::KernelPCA< KernelType, KernelRule >::centerTransformedData\&.
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> bool& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::CenterTransformedData ()\fC [inline]\fP"

.PP
Return whether or not the transformed data is centered\&. 
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Definition at line 127 of file kernel_pca\&.hpp\&.
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References mlpack::kpca::KernelPCA< KernelType, KernelRule >::centerTransformedData\&.
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> const KernelType& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Kernel () const\fC [inline]\fP"

.PP
Get the kernel\&. 
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Definition at line 120 of file kernel_pca\&.hpp\&.
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References mlpack::kpca::KernelPCA< KernelType, KernelRule >::kernel\&.
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> KernelType& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Kernel ()\fC [inline]\fP"

.PP
Modify the kernel\&. 
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Definition at line 122 of file kernel_pca\&.hpp\&.
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References mlpack::kpca::KernelPCA< KernelType, KernelRule >::kernel\&.
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> std::string \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::ToString () const"

.SH "Member Data Documentation"
.PP 
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> bool \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::centerTransformedData\fC [private]\fP"

.PP
If true, the data will be scaled (by standard deviation) when \fBApply()\fP is run\&. 
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Definition at line 137 of file kernel_pca\&.hpp\&.
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Referenced by mlpack::kpca::KernelPCA< KernelType, KernelRule >::CenterTransformedData()\&.
.SS "template<typename KernelType , typename KernelRule  = NaiveKernelRule<KernelType>> KernelType \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::kernel\fC [private]\fP"

.PP
The instantiated kernel\&. 
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Definition at line 134 of file kernel_pca\&.hpp\&.
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Referenced by mlpack::kpca::KernelPCA< KernelType, KernelRule >::Kernel()\&.

.SH "Author"
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Generated automatically by Doxygen for MLPACK from the source code\&.