mlpack::kpca::KernelPCA< KernelType, KernelRule > Class Template Reference

This class performs kernel principal components analysis (Kernel PCA), for a given kernel. More...

#include <kernel_pca.hpp>

Public Member Functions
	KernelPCA (const KernelType kernel=KernelType(), const bool centerTransformedData=false)
	Construct the KernelPCA object, optionally passing a kernel. More...
void	Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec, const size_t newDimension)
	Apply Kernel Principal Components Analysis to the provided data set. More...
void	Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec)
	Apply Kernel Principal Components Analysis to the provided data set. More...
void	Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval)
	Apply Kernel Principal Component Analysis to the provided data set. More...
void	Apply (arma::mat &data, const size_t newDimension)
	Apply dimensionality reduction using Kernel Principal Component Analysis to the provided data set. More...
const KernelType &	Kernel () const
	Get the kernel.
KernelType &	Kernel ()
	Modify the kernel.
bool	CenterTransformedData () const
	Return whether or not the transformed data is centered.
bool &	CenterTransformedData ()
	Return whether or not the transformed data is centered.

Detailed Description

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.

The performance of the method is highly dependent on the kernel choice. There are numerous available kernels in the mlpack::kernel namespace (see files in mlpack/core/kernels/) and it is easy to write your own; see other implementations for examples.

Constructor & Destructor Documentation

KernelPCA()

template<typename KernelType , typename KernelRule >

mlpack::kpca::KernelPCA< KernelType, KernelRule >::KernelPCA	(	const KernelType	kernel = KernelType(),
		const bool	centerTransformedData = false
	)

Construct the KernelPCA 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).

Parameters

kernel	Kernel to be used for computation.
centerTransformedData	Center transformed data.

Member Function Documentation

Apply() [1/4]

template<typename KernelType , typename KernelRule >

void mlpack::kpca::KernelPCA< KernelType, KernelRule >::Apply	(	const arma::mat &	data,
		arma::mat &	transformedData,
		arma::vec &	eigval,
		arma::mat &	eigvec,
		const size_t	newDimension
	)

Apply Kernel Principal Components Analysis to the provided data set.

Apply Kernel Principal Component Analysis to the provided data set.

Parameters

data	Data matrix.
transformedData	Matrix to output results into.
eigval	KPCA eigenvalues will be written to this vector.
eigvec	KPCA eigenvectors will be written to this matrix.
newDimension	New dimension for the dataset.

Apply() [2/4]

template<typename KernelType , typename KernelRule >

void mlpack::kpca::KernelPCA< KernelType, KernelRule >::Apply	(	const arma::mat &	data,
		arma::mat &	transformedData,
		arma::vec &	eigval,
		arma::mat &	eigvec
	)

Apply Kernel Principal Components Analysis to the provided data set.

Apply Kernel Principal Component Analysis to the provided data set.

Parameters

data	Data matrix.
transformedData	Matrix to output results into.
eigval	KPCA eigenvalues will be written to this vector.
eigvec	KPCA eigenvectors will be written to this matrix.

Apply() [3/4]

template<typename KernelType , typename KernelRule >

void mlpack::kpca::KernelPCA< KernelType, KernelRule >::Apply	(	const arma::mat &	data,
		arma::mat &	transformedData,
		arma::vec &	eigval
	)

Apply Kernel Principal Component Analysis to the provided data set.

Parameters

data	Data matrix.
transformedData	Matrix to output results into.
eigval	KPCA eigenvalues will be written to this vector.

Apply() [4/4]

template<typename KernelType , typename KernelRule >

void mlpack::kpca::KernelPCA< KernelType, KernelRule >::Apply	(	arma::mat &	data,
		const size_t	newDimension
	)

Apply dimensionality reduction using Kernel Principal Component Analysis to the provided data set.

Use KPCA for dimensionality reduction.

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"...

Parameters

data	Data matrix.
newDimension	New dimension for the dataset.

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

• src/mlpack/methods/kernel_pca/kernel_pca.hpp
• src/mlpack/methods/kernel_pca/kernel_pca_impl.hpp