The "softmax" stochastic neighbor assignment probability function. More...
Public Member Functions | |
SoftmaxErrorFunction (const arma::mat &dataset, const arma::Col< size_t > &labels, MetricType metric=MetricType()) | |
Initialize with the given kernel; useful when the kernel has some state to store, which is set elsewhere. | |
double | Evaluate (const arma::mat &covariance, const size_t i) |
Evaluate the softmax objective function for the given covariance matrix on only one point of the dataset. | |
double | Evaluate (const arma::mat &covariance) |
Evaluate the softmax function for the given covariance matrix. | |
const arma::mat | GetInitialPoint () const |
Get the initial point. | |
void | Gradient (const arma::mat &covariance, const size_t i, arma::mat &gradient) |
Evaluate the gradient of the softmax function for the given covariance matrix on only one point of the dataset. | |
void | Gradient (const arma::mat &covariance, arma::mat &gradient) |
Evaluate the gradient of the softmax function for the given covariance matrix. | |
size_t | NumFunctions () const |
Get the number of functions the objective function can be decomposed into. | |
Private Member Functions | |
void | Precalculate (const arma::mat &coordinates) |
Precalculate the denominators and numerators that will make up the p_ij, but only if the coordinates matrix is different than the last coordinates the Precalculate() method was run with. | |
Private Attributes | |
const arma::mat & | dataset |
The dataset. | |
arma::vec | denominators |
Holds denominators for calculation of p_ij, for the non-separable Evaluate() and Gradient(). | |
const arma::Col< size_t > & | labels |
Labels for each point in the dataset. | |
arma::mat | lastCoordinates |
Last coordinates. Used for the non-separable Evaluate() and Gradient(). | |
MetricType | metric |
The instantiated metric. | |
arma::vec | p |
Holds calculated p_i, for the non-separable Evaluate() and Gradient(). | |
bool | precalculated |
False if nothing has ever been precalculated (only at construction time). | |
arma::mat | stretchedDataset |
Stretched dataset. Kept internal to avoid memory reallocations. |
The "softmax" stochastic neighbor assignment probability function.
The actual function is
p_ij = (exp(-|| A x_i - A x_j || ^ 2)) / (sum_{k != i} (exp(-|| A x_i - A x_k || ^ 2)))
where x_n represents a point and A is the current scaling matrix.
This class is more flexible than the original paper, allowing an arbitrary metric function to be used in place of || A x_i - A x_j ||^2, meaning that the squared Euclidean distance is not the only allowed metric for NCA. However, that is probably the best way to use this class.
In addition to the standard Evaluate() and Gradient() functions which MLPACK optimizers use, overloads of Evaluate() and Gradient() are given which only operate on one point in the dataset. This is useful for optimizers like stochastic gradient descent (see mlpack::optimization::SGD).
Definition at line 52 of file nca_softmax_error_function.hpp.
mlpack::nca::SoftmaxErrorFunction< MetricType >::SoftmaxErrorFunction | ( | const arma::mat & | dataset, | |
const arma::Col< size_t > & | labels, | |||
MetricType | metric = MetricType() | |||
) |
double mlpack::nca::SoftmaxErrorFunction< MetricType >::Evaluate | ( | const arma::mat & | covariance, | |
const size_t | i | |||
) |
Evaluate the softmax objective function for the given covariance matrix on only one point of the dataset.
This is the separable implementation, where the objective function is decomposed into the sum of many objective functions, and here, only one of those constituent objective functions is returned.
covariance | Covariance matrix of Mahalanobis distance. | |
i | Index of point to use for objective function. |
double mlpack::nca::SoftmaxErrorFunction< MetricType >::Evaluate | ( | const arma::mat & | covariance | ) |
Evaluate the softmax function for the given covariance matrix.
This is the non-separable implementation, where the objective function is not decomposed into the sum of several objective functions.
covariance | Covariance matrix of Mahalanobis distance. |
const arma::mat mlpack::nca::SoftmaxErrorFunction< MetricType >::GetInitialPoint | ( | ) | const |
Get the initial point.
void mlpack::nca::SoftmaxErrorFunction< MetricType >::Gradient | ( | const arma::mat & | covariance, | |
const size_t | i, | |||
arma::mat & | gradient | |||
) |
Evaluate the gradient of the softmax function for the given covariance matrix on only one point of the dataset.
This is the separable implementation, where the objective function is decomposed into the sum of many objective functions, and here, only one of those constituent objective functions is returned.
covariance | Covariance matrix of Mahalanobis distance. | |
i | Index of point to use for objective function. | |
gradient | Matrix to store the calculated gradient in. |
void mlpack::nca::SoftmaxErrorFunction< MetricType >::Gradient | ( | const arma::mat & | covariance, | |
arma::mat & | gradient | |||
) |
Evaluate the gradient of the softmax function for the given covariance matrix.
This is the non-separable implementation, where the objective function is not decomposed into the sum of several objective functions.
covariance | Covariance matrix of Mahalanobis distance. | |
gradient | Matrix to store the calculated gradient in. |
size_t mlpack::nca::SoftmaxErrorFunction< MetricType >::NumFunctions | ( | ) | const [inline] |
Get the number of functions the objective function can be decomposed into.
This is just the number of points in the dataset.
Definition at line 124 of file nca_softmax_error_function.hpp.
void mlpack::nca::SoftmaxErrorFunction< MetricType >::Precalculate | ( | const arma::mat & | coordinates | ) | [private] |
Precalculate the denominators and numerators that will make up the p_ij, but only if the coordinates matrix is different than the last coordinates the Precalculate() method was run with.
This method is only called by the non-separable Evaluate() and Gradient().
This will update last_coordinates_ and stretched_dataset_, and also calculate the p_i and denominators_ which are used in the calculation of p_i or p_ij. The calculation will be O((n * (n + 1)) / 2), which is not great.
coordinates | Coordinates matrix to use for precalculation. |
const arma::mat& mlpack::nca::SoftmaxErrorFunction< MetricType >::dataset [private] |
The dataset.
Definition at line 128 of file nca_softmax_error_function.hpp.
arma::vec mlpack::nca::SoftmaxErrorFunction< MetricType >::denominators [private] |
Holds denominators for calculation of p_ij, for the non-separable Evaluate() and Gradient().
Definition at line 143 of file nca_softmax_error_function.hpp.
const arma::Col<size_t>& mlpack::nca::SoftmaxErrorFunction< MetricType >::labels [private] |
Labels for each point in the dataset.
Definition at line 130 of file nca_softmax_error_function.hpp.
arma::mat mlpack::nca::SoftmaxErrorFunction< MetricType >::lastCoordinates [private] |
Last coordinates. Used for the non-separable Evaluate() and Gradient().
Definition at line 136 of file nca_softmax_error_function.hpp.
MetricType mlpack::nca::SoftmaxErrorFunction< MetricType >::metric [private] |
The instantiated metric.
Definition at line 133 of file nca_softmax_error_function.hpp.
arma::vec mlpack::nca::SoftmaxErrorFunction< MetricType >::p [private] |
Holds calculated p_i, for the non-separable Evaluate() and Gradient().
Definition at line 140 of file nca_softmax_error_function.hpp.
bool mlpack::nca::SoftmaxErrorFunction< MetricType >::precalculated [private] |
False if nothing has ever been precalculated (only at construction time).
Definition at line 146 of file nca_softmax_error_function.hpp.
arma::mat mlpack::nca::SoftmaxErrorFunction< MetricType >::stretchedDataset [private] |
Stretched dataset. Kept internal to avoid memory reallocations.
Definition at line 138 of file nca_softmax_error_function.hpp.