Phpml\DimensionReduction\KernelPCA Class Reference

Inheritance diagram for Phpml\DimensionReduction\KernelPCA:

Public Member Functions
	__construct (int $kernel=self::KERNEL_RBF, ?float $totalVariance=null, ?int $numFeatures=null, ?float $gamma=null)
	Kernel principal component analysis (KernelPCA) is an extension of PCA using techniques of kernel methods.
	fit (array $data)
	Takes a data and returns a lower dimensional version of this data while preserving $totalVariance or $numFeatures.
	transform (array $sample)
	Transforms the given sample to a lower dimensional vector by using the variables obtained during the last run of fit.

Public Attributes
int	$numFeatures = null
	Number of features to be preserved after the reduction.
float	$totalVariance = 0.9
	Total variance to be conserved after the reduction.
const	KERNEL_LAPLACIAN = 3
const	KERNEL_LINEAR = 4
const	KERNEL_RBF = 1
const	KERNEL_SIGMOID = 2

Protected Member Functions
	calculateKernelMatrix (array $data, int $numRows)
	Calculates similarity matrix by use of selected kernel function An n-by-m matrix is given and an n-by-n matrix is returned.
	calculateMeans (array $data, int $n)
	centerMatrix (array $matrix, int $n)
	Kernel matrix is centered in its original space by using the following conversion:
	eigenDecomposition (array $matrix)
	Calculates eigenValues and eigenVectors of the given matrix.
	getDistancePairs (array $sample)
	getKernel ()
	Returns the callable kernel function.
	normalize (array $data, int $n)
	Normalization of the data includes subtracting mean from each dimension therefore dimensions will be centered to zero.
	projectSample (array $pairs)
	reduce (array $data)
	Returns the reduced data.

Protected Attributes
array	$data = []
	Original dataset used to fit KernelPCA.
array	$eigValues = []
	Top eigenValues of the matrix.
array	$eigVectors = []
	Top eigenvectors of the matrix.
bool	$fit = false
float null	$gamma
	Gamma value used by the kernel.
int	$kernel
array	$means = []

Constructor & Destructor Documentation

__construct()

Phpml\DimensionReduction\KernelPCA::__construct	(	int	$kernel = self::KERNEL_RBF,
		?float	$totalVariance = null,
		?int	$numFeatures = null,
		?float	$gamma = null )

Kernel principal component analysis (KernelPCA) is an extension of PCA using techniques of kernel methods.

It is more suitable for data that involves vectors that are not linearly separable

Example: $kpca = new KernelPCA(KernelPCA::KERNEL_RBF, null, 2, 15.0); will initialize the algorithm with an RBF kernel having the gamma parameter as 15,0.
This transformation will return the same number of rows with only 2 columns.

Parameters

float	$totalVariance	Total variance to be preserved if numFeatures is not given
int	$numFeatures	Number of columns to be returned
float	$gamma	Gamma parameter is used with RBF and Sigmoid kernels

Exceptions

InvalidArgumentException

Member Function Documentation

centerMatrix()

Phpml\DimensionReduction\KernelPCA::centerMatrix ( array $matrix, int $n )

protected

Kernel matrix is centered in its original space by using the following conversion:

K′ = K − N.K − K.N + N.K.N where N is n-by-n matrix filled with 1/n

eigenDecomposition()

Phpml\DimensionReduction\EigenTransformerBase::eigenDecomposition ( array $matrix )

protectedinherited

Calculates eigenValues and eigenVectors of the given matrix.

Returns top eigenVectors along with the largest eigenValues. The total explained variance of these eigenVectors will be no less than desired $totalVariance value

fit()

Phpml\DimensionReduction\KernelPCA::fit

(

array

$data

)

Takes a data and returns a lower dimensional version of this data while preserving $totalVariance or $numFeatures.

$data is an n-by-m matrix and returned array is n-by-k matrix where k <= m

Reimplemented from Phpml\DimensionReduction\PCA.

getKernel()

Phpml\DimensionReduction\KernelPCA::getKernel ( )

protected

Returns the callable kernel function.

Exceptions

Exception

transform()

Phpml\DimensionReduction\KernelPCA::transform

(

array

$sample

)

Transforms the given sample to a lower dimensional vector by using the variables obtained during the last run of fit.

Exceptions

InvalidArgumentException
InvalidOperationException

Reimplemented from Phpml\DimensionReduction\PCA.

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

• lib/mlbackend/php/phpml/src/Phpml/DimensionReduction/KernelPCA.php