data::Gram< KERNEL, T > Struct Template Reference

Public Member Functions
	Gram ()
	Default constructor.
template<typename... Ts>
	Gram (Ts &&... args)
	Construct and initialize kernel with arbitrary arguments. More...
arma::Mat< T >	GetMatrix2 (const arma::Mat< T > &input1, const arma::Mat< T > &input2) const
	Compute Gram matrix for row-major ordered data. More...
arma::Mat< T >	GetMatrix (const arma::Mat< T > &input1, const arma::Mat< T > &input2) const
	Compute Gram matrix for column-major ordered data. More...
arma::Mat< T >	GetApprox (const arma::Mat< T > &input1, const arma::Mat< T > &input2, size_t k) const
	Compute an approximate Gram matrix using the Nyström method. More...
arma::Mat< T >	GetMatrix (const arma::Mat< T > &input1) const
	Compute Gram matrix of a dataset with itself (column-major). More...
template<typename Archive >
void	serialize (Archive &ar, const unsigned int)

Public Attributes
KERNEL	kernel_

Detailed Description

template<class KERNEL, class T = DTYPE>
struct data::Gram< KERNEL, T >

Definition at line 136 of file data.h.

Constructor & Destructor Documentation

Gram()

template<class KERNEL , class T = DTYPE>

template<typename... Ts>

data::Gram< KERNEL, T >::Gram ( Ts &&...  args )

inline

Construct and initialize kernel with arbitrary arguments.

Template Parameters

Ts	Argument types for the kernel constructor.

Parameters

args	Arguments to forward to the kernel constructor.

Definition at line 147 of file data.h.

: kernel_(args...) {}

Member Function Documentation

GetApprox()

template<class KERNEL , class T = DTYPE>

arma::Mat<T> data::Gram< KERNEL, T >::GetApprox ( const arma::Mat< T > &  input1, const arma::Mat< T > &  input2, size_t  k  ) const

inline

Compute an approximate Gram matrix using the Nyström method.

Selects k random landmark points, computes their kernel matrix W, and uses it to approximate the full kernel matrix: K_approx = C * pinv(W) * C^T

Parameters

input1	First dataset (columns are samples).
input2	Second dataset (columns are samples).
k	Number of landmark points to sample.

Returns

Approximated Gram matrix.

Definition at line 204 of file data.h.

    {
        size_t n_samples = input1.n_rows;
        arma::uvec indices = arma::randi<arma::uvec>(k, arma::distr_param(0, n_samples - 1));
        arma::Mat<T> landmarks = input1.cols(indices);
 
        arma::Mat<T> W = this->GetMatrix(landmarks, landmarks);
        arma::Mat<T> C = this->GetMatrix(input1, landmarks);
        arma::Mat<T> W_pinv = arma::pinv(W);
 
        return C * W_pinv * C.t();
    }

References data::Gram< KERNEL, T >::GetMatrix().

Here is the call graph for this function:

GetMatrix() [1/2]

template<class KERNEL , class T = DTYPE>

arma::Mat<T> data::Gram< KERNEL, T >::GetMatrix ( const arma::Mat< T > &  input1 ) const

inline

Compute Gram matrix of a dataset with itself (column-major).

Parameters

input1

Dataset (columns are samples).

Returns

Symmetric Gram matrix of size input1.n_cols × input1.n_cols.

Definition at line 224 of file data.h.

    {
        return GetMatrix(input1, input1); 
    }

References data::Gram< KERNEL, T >::GetMatrix().

Here is the call graph for this function:

GetMatrix() [2/2]

template<class KERNEL , class T = DTYPE>

arma::Mat<T> data::Gram< KERNEL, T >::GetMatrix ( const arma::Mat< T > &  input1, const arma::Mat< T > &  input2  ) const

inline

Compute Gram matrix for column-major ordered data.

Parameters

input1	First dataset (columns are samples).
input2	Second dataset (columns are samples).

Returns

Gram matrix of size input1.n_cols × input2.n_cols.

Definition at line 178 of file data.h.

    {
        arma::Mat<T> matrix(input1.n_cols, input2.n_cols);
        
        #pragma omp parallel for collapse(2)
        for (int i = 0; i < int(input1.n_cols); i++)
            for (int j = 0; j < int(input2.n_cols); j++)
                matrix(i,j) = kernel_.Evaluate(input1.col(i).eval(),
                                               input2.col(j).eval());
 
        return matrix;
    }

Referenced by data::Gram< KERNEL, T >::GetApprox(), and data::Gram< KERNEL, T >::GetMatrix().

Here is the caller graph for this function:

GetMatrix2()

template<class KERNEL , class T = DTYPE>

arma::Mat<T> data::Gram< KERNEL, T >::GetMatrix2 ( const arma::Mat< T > &  input1, const arma::Mat< T > &  input2  ) const

inline

Compute Gram matrix for row-major ordered data.

Parameters

input1	First dataset (rows are samples).
input2	Second dataset (rows are samples).

Returns

Gram matrix of size input1.n_rows × input2.n_rows.

Definition at line 158 of file data.h.

    {
        arma::Mat<T> matrix(input1.n_rows, input2.n_rows);
 
        #pragma omp parallel for collapse(2)
        for (int i = 0; i < int(input1.n_rows); i++)
            for (int j = 0; j < int(input2.n_rows); j++)
                matrix(i,j) = kernel_.Evaluate(input1.row(i).eval(),
                                               input2.row(j).eval());
 
        return matrix;
    }

serialize()

template<class KERNEL , class T = DTYPE>

template<typename Archive >

void data::Gram< KERNEL, T >::serialize ( Archive &  ar, const unsigned int    )

inline

Serialize the model.

Definition at line 232 of file data.h.

    {
      ar ( cereal::make_nvp("kernel",kernel_) );
    }

---

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

• data.h