MLPACK  1.0.10
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mlpack::gmm::GMM< FittingType > Class Template Reference

A Gaussian Mixture Model (GMM). More...

Public Member Functions

 GMM ()
 Create an empty Gaussian Mixture Model, with zero gaussians. More...
 
 GMM (const size_t gaussians, const size_t dimensionality)
 Create a GMM with the given number of Gaussians, each of which have the specified dimensionality. More...
 
 GMM (const size_t gaussians, const size_t dimensionality, FittingType &fitter)
 Create a GMM with the given number of Gaussians, each of which have the specified dimensionality. More...
 
 GMM (const std::vector< arma::vec > &means, const std::vector< arma::mat > &covariances, const arma::vec &weights)
 Create a GMM with the given means, covariances, and weights. More...
 
 GMM (const std::vector< arma::vec > &means, const std::vector< arma::mat > &covariances, const arma::vec &weights, FittingType &fitter)
 Create a GMM with the given means, covariances, and weights, and use the given initialized FittingType class. More...
 
template<typename OtherFittingType >
 GMM (const GMM< OtherFittingType > &other)
 Copy constructor for GMMs which use different fitting types. More...
 
 GMM (const GMM &other)
 Copy constructor for GMMs using the same fitting type. More...
 
void Classify (const arma::mat &observations, arma::Col< size_t > &labels) const
 Classify the given observations as being from an individual component in this GMM. More...
 
const std::vector< arma::mat > & Covariances () const
 Return a const reference to the vector of covariance matrices (sigma). More...
 
std::vector< arma::mat > & Covariances ()
 Return a reference to the vector of covariance matrices (sigma). More...
 
size_t Dimensionality () const
 Return the dimensionality of the model. More...
 
size_t & Dimensionality ()
 Modify the dimensionality of the model. More...
 
double Estimate (const arma::mat &observations, const size_t trials=1, const bool useExistingModel=false)
 Estimate the probability distribution directly from the given observations, using the given algorithm in the FittingType class to fit the data. More...
 
double Estimate (const arma::mat &observations, const arma::vec &probabilities, const size_t trials=1, const bool useExistingModel=false)
 Estimate the probability distribution directly from the given observations, taking into account the probability of each observation actually being from this distribution, and using the given algorithm in the FittingType class to fit the data. More...
 
const FittingType & Fitter () const
 Return a const reference to the fitting type. More...
 
FittingType & Fitter ()
 Return a reference to the fitting type. More...
 
size_t Gaussians () const
 Return the number of gaussians in the model. More...
 
size_t & Gaussians ()
 Modify the number of gaussians in the model. More...
 
void Load (const std::string &filename)
 Load a GMM from an XML file. More...
 
const std::vector< arma::vec > & Means () const
 Return a const reference to the vector of means (mu). More...
 
std::vector< arma::vec > & Means ()
 Return a reference to the vector of means (mu). More...
 
template<typename OtherFittingType >
GMMoperator= (const GMM< OtherFittingType > &other)
 Copy operator for GMMs which use different fitting types. More...
 
GMMoperator= (const GMM &other)
 Copy operator for GMMs which use the same fitting type. More...
 
double Probability (const arma::vec &observation) const
 Return the probability that the given observation came from this distribution. More...
 
double Probability (const arma::vec &observation, const size_t component) const
 Return the probability that the given observation came from the given Gaussian component in this distribution. More...
 
arma::vec Random () const
 Return a randomly generated observation according to the probability distribution defined by this object. More...
 
void Save (const std::string &filename) const
 Save a GMM to an XML file. More...
 
std::string ToString () const
 Returns a string representation of this object. More...
 
const arma::vec & Weights () const
 Return a const reference to the a priori weights of each Gaussian. More...
 
arma::vec & Weights ()
 Return a reference to the a priori weights of each Gaussian. More...
 

Private Member Functions

double LogLikelihood (const arma::mat &dataPoints, const std::vector< arma::vec > &means, const std::vector< arma::mat > &covars, const arma::vec &weights) const
 This function computes the loglikelihood of the given model. More...
 

Private Attributes

std::vector< arma::mat > covariances
 Vector of covariances; one for each Gaussian. More...
 
size_t dimensionality
 The dimensionality of the model. More...
 
FittingType & fitter
 Reference to the fitting object we should use. More...
 
size_t gaussians
 The number of Gaussians in the model. More...
 
FittingType localFitter
 Locally-stored fitting object; in case the user did not pass one. More...
 
std::vector< arma::vec > means
 Vector of means; one for each Gaussian. More...
 
arma::vec weights
 Vector of a priori weights for each Gaussian. More...
 

Detailed Description

template<typename FittingType = EMFit<>>
class mlpack::gmm::GMM< FittingType >

A Gaussian Mixture Model (GMM).

This class uses maximum likelihood loss functions to estimate the parameters of the GMM on a given dataset via the given fitting mechanism, defined by the FittingType template parameter. The GMM can be trained using normal data, or data with probabilities of being from this GMM (see GMM::Estimate() for more information).

The FittingType template class must provide a way for the GMM to train on data. It must provide the following two functions:

void Estimate(const arma::mat& observations,
std::vector<arma::vec>& means,
std::vector<arma::mat>& covariances,
arma::vec& weights);
void Estimate(const arma::mat& observations,
const arma::vec& probabilities,
std::vector<arma::vec>& means,
std::vector<arma::mat>& covariances,
arma::vec& weights);

These functions should produce a trained GMM from the given observations and probabilities. These may modify the size of the model (by increasing the size of the mean and covariance vectors as well as the weight vectors), but the method should expect that these vectors are already set to the size of the GMM as specified in the constructor.

For a sample implementation, see the EMFit class; this class uses the EM algorithm to train a GMM, and is the default fitting type.

The GMM, once trained, can be used to generate random points from the distribution and estimate the probability of points being from the distribution. The parameters of the GMM can be obtained through the accessors and mutators.

Example use:

// Set up a mixture of 5 gaussians in a 4-dimensional space (uses the default
// EM fitting mechanism).
GMM<> g(5, 4);
// Train the GMM given the data observations.
g.Estimate(data);
// Get the probability of 'observation' being observed from this GMM.
double probability = g.Probability(observation);
// Get a random observation from the GMM.
arma::vec observation = g.Random();

Definition at line 89 of file gmm.hpp.

Constructor & Destructor Documentation

template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( )
inline

Create an empty Gaussian Mixture Model, with zero gaussians.

Definition at line 107 of file gmm.hpp.

References mlpack::Log::Debug.

template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( const size_t  gaussians,
const size_t  dimensionality 
)

Create a GMM with the given number of Gaussians, each of which have the specified dimensionality.

The means and covariances will be set to 0.

Parameters
gaussiansNumber of Gaussians in this GMM.
dimensionalityDimensionality of each Gaussian.
template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( const size_t  gaussians,
const size_t  dimensionality,
FittingType &  fitter 
)

Create a GMM with the given number of Gaussians, each of which have the specified dimensionality.

Also, pass in an initialized FittingType class; this is useful in cases where the FittingType class needs to store some state.

Parameters
gaussiansNumber of Gaussians in this GMM.
dimensionalityDimensionality of each Gaussian.
fitterInitialized fitting mechanism.
template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( const std::vector< arma::vec > &  means,
const std::vector< arma::mat > &  covariances,
const arma::vec &  weights 
)
inline

Create a GMM with the given means, covariances, and weights.

Parameters
meansMeans of the model.
covariancesCovariances of the model.
weightsWeights of the model.

Definition at line 150 of file gmm.hpp.

template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( const std::vector< arma::vec > &  means,
const std::vector< arma::mat > &  covariances,
const arma::vec &  weights,
FittingType &  fitter 
)
inline

Create a GMM with the given means, covariances, and weights, and use the given initialized FittingType class.

This is useful in cases where the FittingType class needs to store some state.

Parameters
meansMeans of the model.
covariancesCovariances of the model.
weightsWeights of the model.

Definition at line 170 of file gmm.hpp.

template<typename FittingType = EMFit<>>
template<typename OtherFittingType >
mlpack::gmm::GMM< FittingType >::GMM ( const GMM< OtherFittingType > &  other)

Copy constructor for GMMs which use different fitting types.

template<typename FittingType = EMFit<>>
mlpack::gmm::GMM< FittingType >::GMM ( const GMM< FittingType > &  other)

Copy constructor for GMMs using the same fitting type.

This also copies the fitter.

Member Function Documentation

template<typename FittingType = EMFit<>>
void mlpack::gmm::GMM< FittingType >::Classify ( const arma::mat &  observations,
arma::Col< size_t > &  labels 
) const

Classify the given observations as being from an individual component in this GMM.

The resultant classifications are stored in the 'labels' object, and each label will be between 0 and (Gaussians() - 1). Supposing that a point was classified with label 2, and that our GMM object was called 'gmm', one could access the relevant Gaussian distribution as follows:

arma::vec mean = gmm.Means()[2];
arma::mat covariance = gmm.Covariances()[2];
double priorWeight = gmm.Weights()[2];
Parameters
observationsList of observations to classify.
labelsObject which will be filled with labels.
template<typename FittingType = EMFit<>>
const std::vector<arma::mat>& mlpack::gmm::GMM< FittingType >::Covariances ( ) const
inline

Return a const reference to the vector of covariance matrices (sigma).

Definition at line 238 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::covariances.

template<typename FittingType = EMFit<>>
std::vector<arma::mat>& mlpack::gmm::GMM< FittingType >::Covariances ( )
inline

Return a reference to the vector of covariance matrices (sigma).

Definition at line 240 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::covariances.

template<typename FittingType = EMFit<>>
size_t mlpack::gmm::GMM< FittingType >::Dimensionality ( ) const
inline

Return the dimensionality of the model.

Definition at line 227 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::dimensionality.

template<typename FittingType = EMFit<>>
size_t& mlpack::gmm::GMM< FittingType >::Dimensionality ( )
inline

Modify the dimensionality of the model.

Careful! You will have to update each mean and covariance matrix yourself.

Definition at line 230 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::dimensionality.

template<typename FittingType = EMFit<>>
double mlpack::gmm::GMM< FittingType >::Estimate ( const arma::mat &  observations,
const size_t  trials = 1,
const bool  useExistingModel = false 
)

Estimate the probability distribution directly from the given observations, using the given algorithm in the FittingType class to fit the data.

The fitting will be performed 'trials' times; from these trials, the model with the greatest log-likelihood will be selected. By default, only one trial is performed. The log-likelihood of the best fitting is returned.

Optionally, the existing model can be used as an initial model for the estimation by setting 'useExistingModel' to true. If the fitting procedure is deterministic after the initial position is given, then 'trials' should be set to 1.

Template Parameters
FittingTypeThe type of fitting method which should be used (EMFit<> is suggested).
Parameters
observationsObservations of the model.
trialsNumber of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModelIf true, the existing model is used as an initial model for the estimation.
Returns
The log-likelihood of the best fit.
template<typename FittingType = EMFit<>>
double mlpack::gmm::GMM< FittingType >::Estimate ( const arma::mat &  observations,
const arma::vec &  probabilities,
const size_t  trials = 1,
const bool  useExistingModel = false 
)

Estimate the probability distribution directly from the given observations, taking into account the probability of each observation actually being from this distribution, and using the given algorithm in the FittingType class to fit the data.

The fitting will be performed 'trials' times; from these trials, the model with the greatest log-likelihood will be selected. By default, only one trial is performed. The log-likelihood of the best fitting is returned.

Optionally, the existing model can be used as an initial model for the estimation by setting 'useExistingModel' to true. If the fitting procedure is deterministic after the initial position is given, then 'trials' should be set to 1.

Parameters
observationsObservations of the model.
probabilitiesProbability of each observation being from this distribution.
trialsNumber of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModelIf true, the existing model is used as an initial model for the estimation.
Returns
The log-likelihood of the best fit.
template<typename FittingType = EMFit<>>
const FittingType& mlpack::gmm::GMM< FittingType >::Fitter ( ) const
inline

Return a const reference to the fitting type.

Definition at line 248 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::fitter.

template<typename FittingType = EMFit<>>
FittingType& mlpack::gmm::GMM< FittingType >::Fitter ( )
inline

Return a reference to the fitting type.

Definition at line 250 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::fitter.

template<typename FittingType = EMFit<>>
size_t mlpack::gmm::GMM< FittingType >::Gaussians ( ) const
inline

Return the number of gaussians in the model.

Definition at line 221 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::gaussians.

template<typename FittingType = EMFit<>>
size_t& mlpack::gmm::GMM< FittingType >::Gaussians ( )
inline

Modify the number of gaussians in the model.

Careful! You will have to resize the means, covariances, and weights yourself.

Definition at line 224 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::gaussians.

template<typename FittingType = EMFit<>>
void mlpack::gmm::GMM< FittingType >::Load ( const std::string &  filename)

Load a GMM from an XML file.

The format of the XML file should be the same as is generated by the Save() method.

Parameters
filenameName of XML file containing model to be loaded.
template<typename FittingType = EMFit<>>
double mlpack::gmm::GMM< FittingType >::LogLikelihood ( const arma::mat &  dataPoints,
const std::vector< arma::vec > &  means,
const std::vector< arma::mat > &  covars,
const arma::vec &  weights 
) const
private

This function computes the loglikelihood of the given model.

This function is used by GMM::Estimate().

Parameters
dataPointsObservations to calculate the likelihood for.
meansMeans of the given mixture model.
covarsCovariances of the given mixture model.
weightsWeights of the given mixture model.
template<typename FittingType = EMFit<>>
const std::vector<arma::vec>& mlpack::gmm::GMM< FittingType >::Means ( ) const
inline

Return a const reference to the vector of means (mu).

Definition at line 233 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::means.

template<typename FittingType = EMFit<>>
std::vector<arma::vec>& mlpack::gmm::GMM< FittingType >::Means ( )
inline

Return a reference to the vector of means (mu).

Definition at line 235 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::means.

template<typename FittingType = EMFit<>>
template<typename OtherFittingType >
GMM& mlpack::gmm::GMM< FittingType >::operator= ( const GMM< OtherFittingType > &  other)

Copy operator for GMMs which use different fitting types.

template<typename FittingType = EMFit<>>
GMM& mlpack::gmm::GMM< FittingType >::operator= ( const GMM< FittingType > &  other)

Copy operator for GMMs which use the same fitting type.

This also copies the fitter.

template<typename FittingType = EMFit<>>
double mlpack::gmm::GMM< FittingType >::Probability ( const arma::vec &  observation) const

Return the probability that the given observation came from this distribution.

Parameters
observationObservation to evaluate the probability of.
template<typename FittingType = EMFit<>>
double mlpack::gmm::GMM< FittingType >::Probability ( const arma::vec &  observation,
const size_t  component 
) const

Return the probability that the given observation came from the given Gaussian component in this distribution.

Parameters
observationObservation to evaluate the probability of.
componentIndex of the component of the GMM to be considered.
template<typename FittingType = EMFit<>>
arma::vec mlpack::gmm::GMM< FittingType >::Random ( ) const

Return a randomly generated observation according to the probability distribution defined by this object.

Returns
Random observation from this GMM.
template<typename FittingType = EMFit<>>
void mlpack::gmm::GMM< FittingType >::Save ( const std::string &  filename) const

Save a GMM to an XML file.

Parameters
filenameName of XML file to write to.
template<typename FittingType = EMFit<>>
std::string mlpack::gmm::GMM< FittingType >::ToString ( ) const

Returns a string representation of this object.

template<typename FittingType = EMFit<>>
const arma::vec& mlpack::gmm::GMM< FittingType >::Weights ( ) const
inline

Return a const reference to the a priori weights of each Gaussian.

Definition at line 243 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::weights.

template<typename FittingType = EMFit<>>
arma::vec& mlpack::gmm::GMM< FittingType >::Weights ( )
inline

Return a reference to the a priori weights of each Gaussian.

Definition at line 245 of file gmm.hpp.

References mlpack::gmm::GMM< FittingType >::weights.

Member Data Documentation

template<typename FittingType = EMFit<>>
std::vector<arma::mat> mlpack::gmm::GMM< FittingType >::covariances
private

Vector of covariances; one for each Gaussian.

Definition at line 99 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Covariances().

template<typename FittingType = EMFit<>>
size_t mlpack::gmm::GMM< FittingType >::dimensionality
private

The dimensionality of the model.

Definition at line 95 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Dimensionality().

template<typename FittingType = EMFit<>>
FittingType& mlpack::gmm::GMM< FittingType >::fitter
private

Reference to the fitting object we should use.

Definition at line 376 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Fitter().

template<typename FittingType = EMFit<>>
size_t mlpack::gmm::GMM< FittingType >::gaussians
private

The number of Gaussians in the model.

Definition at line 93 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Gaussians().

template<typename FittingType = EMFit<>>
FittingType mlpack::gmm::GMM< FittingType >::localFitter
private

Locally-stored fitting object; in case the user did not pass one.

Definition at line 373 of file gmm.hpp.

template<typename FittingType = EMFit<>>
std::vector<arma::vec> mlpack::gmm::GMM< FittingType >::means
private

Vector of means; one for each Gaussian.

Definition at line 97 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Means().

template<typename FittingType = EMFit<>>
arma::vec mlpack::gmm::GMM< FittingType >::weights
private

Vector of a priori weights for each Gaussian.

Definition at line 101 of file gmm.hpp.

Referenced by mlpack::gmm::GMM< FittingType >::Weights().


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