This class performs kernel principal components analysis (Kernel PCA), for a given kernel. More...
Public Member Functions | |
KernelPCA (const KernelType kernel=KernelType(), const bool centerTransformedData=false) | |
Construct the KernelPCA object, optionally passing a kernel. | |
void | Apply (arma::mat &data, const size_t newDimension) |
Apply dimensionality reduction using Kernel Principal Component 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 (const arma::mat &data, arma::mat &transformedData, arma::vec &eigval, arma::mat &eigvec) |
Apply Kernel Principal Components Analysis to the provided data set. | |
bool & | CenterTransformedData () |
Return whether or not the transformed data is centered. | |
bool | CenterTransformedData () const |
Return whether or not the transformed data is centered. | |
KernelType & | Kernel () |
Modify the kernel. | |
const KernelType & | Kernel () const |
Get the kernel. | |
Private Member Functions | |
void | GetKernelMatrix (const arma::mat &data, arma::mat &kernelMatrix) |
Construct the kernel matrix. | |
Private Attributes | |
bool | centerTransformedData |
If true, the data will be scaled (by standard deviation) when Apply() is run. | |
KernelType | kernel |
The instantiated kernel. |
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 46 of file kernel_pca.hpp.
mlpack::kpca::KernelPCA< KernelType >::KernelPCA | ( | const KernelType | kernel = KernelType() , |
|
const bool | centerTransformedData = false | |||
) |
void mlpack::kpca::KernelPCA< KernelType >::Apply | ( | arma::mat & | data, | |
const size_t | newDimension | |||
) |
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"...
data | Data matrix. | |
newDimension | New dimension for the dataset. |
void mlpack::kpca::KernelPCA< KernelType >::Apply | ( | const arma::mat & | data, | |
arma::mat & | transformedData, | |||
arma::vec & | eigval | |||
) |
void mlpack::kpca::KernelPCA< KernelType >::Apply | ( | const arma::mat & | data, | |
arma::mat & | transformedData, | |||
arma::vec & | eigval, | |||
arma::mat & | eigvec | |||
) |
bool& mlpack::kpca::KernelPCA< KernelType >::CenterTransformedData | ( | ) | [inline] |
Return whether or not the transformed data is centered.
Definition at line 107 of file kernel_pca.hpp.
References mlpack::kpca::KernelPCA< KernelType >::centerTransformedData.
bool mlpack::kpca::KernelPCA< KernelType >::CenterTransformedData | ( | ) | const [inline] |
Return whether or not the transformed data is centered.
Definition at line 105 of file kernel_pca.hpp.
References mlpack::kpca::KernelPCA< KernelType >::centerTransformedData.
void mlpack::kpca::KernelPCA< KernelType >::GetKernelMatrix | ( | const arma::mat & | data, | |
arma::mat & | kernelMatrix | |||
) | [private] |
KernelType& mlpack::kpca::KernelPCA< KernelType >::Kernel | ( | ) | [inline] |
Modify the kernel.
Definition at line 102 of file kernel_pca.hpp.
References mlpack::kpca::KernelPCA< KernelType >::kernel.
const KernelType& mlpack::kpca::KernelPCA< KernelType >::Kernel | ( | ) | const [inline] |
Get the kernel.
Definition at line 100 of file kernel_pca.hpp.
References mlpack::kpca::KernelPCA< KernelType >::kernel.
bool mlpack::kpca::KernelPCA< KernelType >::centerTransformedData [private] |
If true, the data will be scaled (by standard deviation) when Apply() is run.
Definition at line 114 of file kernel_pca.hpp.
Referenced by mlpack::kpca::KernelPCA< KernelType >::CenterTransformedData().
KernelType mlpack::kpca::KernelPCA< KernelType >::kernel [private] |
The instantiated kernel.
Definition at line 111 of file kernel_pca.hpp.
Referenced by mlpack::kpca::KernelPCA< KernelType >::Kernel().