mlpack_kpca_KernelPCA (3)

Public Member Functions

KernelPCA (const KernelType kernel=KernelType(), const bool centerTransformedData=false)

Construct the KernelPCA object, optionally passing a kernel. 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. 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. void Apply (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval)

Apply Kernel Principal Component Analysis to the provided data set. void Apply (arma::mat &data, const size_t newDimension)

Apply dimensionality reduction using Kernel Principal Component Analysis to the provided data set. bool CenterTransformedData () const

Return whether or not the transformed data is centered. bool & CenterTransformedData ()

Return whether or not the transformed data is centered. const KernelType & Kernel () const

Get the kernel. KernelType & Kernel ()

Modify the kernel. std::string ToString () const

Private Attributes

bool centerTransformedData

If true, the data will be scaled (by standard deviation) when Apply() is run. KernelType kernel

The instantiated kernel.

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.

Definition at line 50 of file kernel_pca.hpp.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::\fBKernelPCA\fP (const KernelTypekernel = \fCKernelType()\fP, const boolcenterTransformedData = \fCfalse\fP)

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.

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)

Apply Kernel Principal Components 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.

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)

Apply Kernel Principal Components 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.

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)

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.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> void \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Apply (arma::mat &data, const size_tnewDimension)

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'...

Parameters:

data Data matrix.

newDimension New dimension for the dataset.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> bool \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::CenterTransformedData () const\fC [inline]\fP

Return whether or not the transformed data is centered.

Definition at line 125 of file kernel_pca.hpp.

References mlpack::kpca::KernelPCA< KernelType, KernelRule >::centerTransformedData.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> bool& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::CenterTransformedData ()\fC [inline]\fP

Return whether or not the transformed data is centered.

Definition at line 127 of file kernel_pca.hpp.

References mlpack::kpca::KernelPCA< KernelType, KernelRule >::centerTransformedData.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> const KernelType& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Kernel () const\fC [inline]\fP

Get the kernel.

Definition at line 120 of file kernel_pca.hpp.

References mlpack::kpca::KernelPCA< KernelType, KernelRule >::kernel.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> KernelType& \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::Kernel ()\fC [inline]\fP

Modify the kernel.

Definition at line 122 of file kernel_pca.hpp.

References mlpack::kpca::KernelPCA< KernelType, KernelRule >::kernel.

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> std::string \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::ToString () const

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> bool \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::centerTransformedData\fC [private]\fP

If true, the data will be scaled (by standard deviation) when Apply() is run.

Definition at line 137 of file kernel_pca.hpp.

Referenced by mlpack::kpca::KernelPCA< KernelType, KernelRule >::CenterTransformedData().

template<typename KernelType , typename KernelRule = NaiveKernelRule<KernelType>> KernelType \fBmlpack::kpca::KernelPCA\fP< KernelType, KernelRule >::kernel\fC [private]\fP

The instantiated kernel.

Definition at line 134 of file kernel_pca.hpp.

Referenced by mlpack::kpca::KernelPCA< KernelType, KernelRule >::Kernel().

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