The "softmax" stochastic neighbor assignment probability function. More...
Public Member Functions  
SoftmaxErrorFunction (const arma::mat &dataset, const arma::Row< size_t > &labels, MetricType metric=MetricType())  
Initialize with the given kernel; useful when the kernel has some state to store, which is set elsewhere. More...  
double  Evaluate (const arma::mat &covariance) 
Evaluate the softmax function for the given covariance matrix. More...  
double  Evaluate (const arma::mat &covariance, const size_t begin, const size_t batchSize=1) 
Evaluate the softmax objective function for the given covariance matrix on the given batch size from a given inital point of the dataset. More...  
const arma::mat  GetInitialPoint () const 
Get the initial point. More...  
void  Gradient (const arma::mat &covariance, arma::mat &gradient) 
Evaluate the gradient of the softmax function for the given covariance matrix. More...  
template < typename GradType >  
void  Gradient (const arma::mat &covariance, const size_t begin, GradType &gradient, const size_t batchSize=1) 
Evaluate the gradient of the softmax function for the given covariance matrix on the given batch size, from a given initial point of the dataset. More...  
size_t  NumFunctions () const 
Get the number of functions the objective function can be decomposed into. More...  
void  Shuffle () 
Shuffle the dataset. More...  
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 43 of file nca_softmax_error_function.hpp.
SoftmaxErrorFunction  (  const arma::mat &  dataset, 
const arma::Row< size_t > &  labels,  
MetricType  metric = MetricType() 

) 
Initialize with the given kernel; useful when the kernel has some state to store, which is set elsewhere.
If no kernel is given, an empty kernel is used; this way, you can call the constructor with no arguments. A reference to the dataset we will be optimizing over is also required.
dataset  Matrix containing the dataset. 
labels  Vector of class labels for each point in the dataset. 
kernel  Instantiated kernel (optional). 
double Evaluate  (  const arma::mat &  covariance  ) 
Evaluate the softmax function for the given covariance matrix.
This is the nonseparable implementation, where the objective function is not decomposed into the sum of several objective functions.
covariance  Covariance matrix of Mahalanobis distance. 
double Evaluate  (  const arma::mat &  covariance, 
const size_t  begin,  
const size_t  batchSize = 1 

) 
Evaluate the softmax objective function for the given covariance matrix on the given batch size from a given inital 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. 
begin  Index of the initial point to use for objective function. 
batchSize  Number of points to use for objective function. 
const arma::mat GetInitialPoint  (  )  const 
Get the initial point.
void Gradient  (  const arma::mat &  covariance, 
arma::mat &  gradient  
) 
Evaluate the gradient of the softmax function for the given covariance matrix.
This is the nonseparable 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. 
void Gradient  (  const arma::mat &  covariance, 
const size_t  begin,  
GradType &  gradient,  
const size_t  batchSize = 1 

) 
Evaluate the gradient of the softmax function for the given covariance matrix on the given batch size, from a given initial 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. The type of the gradient parameter is a template argument to allow the computation of a sparse gradient.
GradType  The type of the gradient outparam. 
covariance  Covariance matrix of Mahalanobis distance. 
begin  Index of the initial point to use for objective function. 
batchSize  Number of points to use for objective function. 
gradient  Matrix to store the calculated gradient in. 

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 130 of file nca_softmax_error_function.hpp.
void Shuffle  (  ) 
Shuffle the dataset.