theplu::yat::utility::KernelPCA Class Reference

Principal Component Analysis on a Kernel Matrix. More...

#include <yat/utility/KernelPCA.h>

List of all members.

Public Member Functions
	KernelPCA (const Matrix &kernel)
virtual	~KernelPCA (void)
	destructor
const Vector &	eigenvalues (void) const
	sorted eigenvalues.
const Matrix &	projection (void) const

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Detailed Description

Principal Component Analysis on a Kernel Matrix.

This class performs PCA on a kernel matrix. Note that this class does not diagonalize the kernel matrix to find eigen-samples that maximizes the variance (use class SVD). Instead, this class finds eigen-features that maximizes the variance in feature space and projects the data onto these eigen-features.

As the covariance of features is not available nor is the data, we create a data matrix Z that fulfills Kernel = Z' * Z. As this data matrix Z has the same kernel matrix as the original data and thus also same distances between each pair of sample, the difference between Z and original data matrix is at most a rotation and translation. Hence, the projection of Z onto the first principial components will be equivalent to the projection of original data onto its principal components.

See also:

PCA

Since:

New in yat 0.7

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Constructor & Destructor Documentation

theplu::yat::utility::KernelPCA::KernelPCA ( const Matrix &  kernel )

explicit

Constructor taking the kernel matrix as input. kernel is expected to be symmetric and positive semi-definite.

The kernel matrix contains the scalar product between all samples, i.e., element kernel(i,j) is the scalar product between sample i and sample j.

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Member Function Documentation

const Vector& theplu::yat::utility::KernelPCA::eigenvalues

(

void

)

const

sorted eigenvalues.

Returns:

eigenvalues sorted such eignenvalues(0) is the largest value

const Matrix& theplu::yat::utility::KernelPCA::projection

(

void

)

const

This function will project data onto the new coordinate-system.

Each column corresponds to a sample.

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

• yat/utility/KernelPCA.h