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 std::vector< distribution::GaussianDistribution > &dists, const arma::vec &weights)
	Create a GMM with the given dists and weights. More...

	GMM (const GMM &other)
	Copy constructor for GMMs. More...

void	Classify (const arma::mat &observations, arma::Row< size_t > &labels) const
	Classify the given observations as being from an individual component in this GMM. More...

const distribution::GaussianDistribution &	Component (size_t i) const
	Return a const reference to a component distribution. More...

distribution::GaussianDistribution &	Component (size_t i)
	Return a reference to a component distribution. More...

size_t	Dimensionality () const
	Return the dimensionality of the model. More...

size_t	Gaussians () const
	Return the number of gaussians in the model. More...

GMM &	operator= (const GMM &other)
	Copy operator for GMMs. 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...

template<typename Archive >
void	Serialize (Archive &ar, const unsigned int)
	Serialize the GMM. More...

template<typename FittingType = EMFit<>>
double	Train (const arma::mat &observations, const size_t trials=1, const bool useExistingModel=false, FittingType fitter=FittingType())
	Estimate the probability distribution directly from the given observations, using the given algorithm in the FittingType class to fit the data. More...

template<typename FittingType = EMFit<>>
double	Train (const arma::mat &observations, const arma::vec &probabilities, const size_t trials=1, const bool useExistingModel=false, FittingType fitter=FittingType())
	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 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< distribution::GaussianDistribution > &distsL, const arma::vec &weights) const
	This function computes the loglikelihood of the given model. More...

Private Attributes
size_t	dimensionality
	The dimensionality of the model. More...

std::vector< distribution::GaussianDistribution >	dists
	Vector of Gaussians. More...

size_t	gaussians
	The number of Gaussians in the model. More...

arma::vec	weights
	Vector of a priori weights for each Gaussian. More...

Detailed Description

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::Train() for more information).

The Train() method uses a template type 'FittingType'. 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<distribution::GaussianDistribution>& dists,
              arma::vec& weights);
void Estimate(const arma::mat& observations,
              const arma::vec& probabilities,
              std::vector<distribution::GaussianDistribution>& dists,
              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 for the Train() method.

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.
GMM g(5, 4);
// Train the GMM given the data observations, using the default EM fitting
// mechanism.
g.Train(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 79 of file gmm.hpp.

Constructor & Destructor Documentation

mlpack::gmm::GMM::GMM ( )

inline

Create an empty Gaussian Mixture Model, with zero gaussians.

Definition at line 97 of file gmm.hpp.

References mlpack::Log::Debug.

Referenced by GMM().

mlpack::gmm::GMM::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

gaussians	Number of Gaussians in this GMM.
dimensionality	Dimensionality of each Gaussian.

mlpack::gmm::GMM::GMM	(	const std::vector< distribution::GaussianDistribution > &	dists,
		const arma::vec &	weights
	)

inline

Create a GMM with the given dists and weights.

Parameters

dists	Distributions of the model.
weights	Weights of the model.

Definition at line 123 of file gmm.hpp.

References GMM(), and operator=().

mlpack::gmm::GMM::GMM ( const GMM & other )

Copy constructor for GMMs.

Member Function Documentation

void mlpack::gmm::GMM::Classify	(	const arma::mat &	observations,
		arma::Row< 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

observations	List of observations to classify.
labels	Object which will be filled with labels.

Referenced by Weights().

const distribution::GaussianDistribution& mlpack::gmm::GMM::Component ( size_t i ) const

inline

Return a const reference to a component distribution.

Parameters

i	index of component.

Definition at line 146 of file gmm.hpp.

distribution::GaussianDistribution& mlpack::gmm::GMM::Component ( size_t i )

inline

Return a reference to a component distribution.

Parameters

i	index of component.

Definition at line 153 of file gmm.hpp.

size_t mlpack::gmm::GMM::Dimensionality ( ) const

inline

Return the dimensionality of the model.

Definition at line 139 of file gmm.hpp.

References dimensionality.

size_t mlpack::gmm::GMM::Gaussians ( ) const

inline

Return the number of gaussians in the model.

Definition at line 137 of file gmm.hpp.

References gaussians.

double mlpack::gmm::GMM::LogLikelihood	(	const arma::mat &	dataPoints,
		const std::vector< distribution::GaussianDistribution > &	distsL,
		const arma::vec &	weights
	)		const

private

This function computes the loglikelihood of the given model.

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

Parameters

dataPoints	Observations to calculate the likelihood for.
means	Means of the given mixture model.
covars	Covariances of the given mixture model.
weights	Weights of the given mixture model.

Referenced by Weights().

GMM& mlpack::gmm::GMM::operator= ( const GMM & other )

Copy operator for GMMs.

Referenced by GMM().

double mlpack::gmm::GMM::Probability ( const arma::vec & observation ) const

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

Parameters

observation Observation to evaluate the probability of.

Referenced by Weights().

double mlpack::gmm::GMM::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

observation	Observation to evaluate the probability of.
component	Index of the component of the GMM to be considered.

arma::vec mlpack::gmm::GMM::Random ( ) const

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

Returns: Random observation from this GMM.

Referenced by Weights().

template<typename Archive >

void mlpack::gmm::GMM::Serialize	(	Archive &	ar,
		const unsigned	int
	)

Serialize the GMM.

Referenced by Weights().

template<typename FittingType = EMFit<>>

double mlpack::gmm::GMM::Train	(	const arma::mat &	observations,
		const size_t	trials = `1`,
		const bool	useExistingModel = `false`,
		FittingType	fitter = `FittingType()`
	)

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

FittingType The type of fitting method which should be used (EMFit<> is suggested).

Parameters

observations	Observations of the model.
trials	Number of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModel	If true, the existing model is used as an initial model for the estimation.

Returns: The log-likelihood of the best fit.

Referenced by Weights().

template<typename FittingType = EMFit<>>

double mlpack::gmm::GMM::Train	(	const arma::mat &	observations,
		const arma::vec &	probabilities,
		const size_t	trials = `1`,
		const bool	useExistingModel = `false`,
		FittingType	fitter = `FittingType()`
	)

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

observations	Observations of the model.
probabilities	Probability of each observation being from this distribution.
trials	Number of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModel	If true, the existing model is used as an initial model for the estimation.

Returns: The log-likelihood of the best fit.

const arma::vec& mlpack::gmm::GMM::Weights ( ) const

inline

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

Definition at line 156 of file gmm.hpp.

References weights.

arma::vec& mlpack::gmm::GMM::Weights ( )

inline

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

Definition at line 158 of file gmm.hpp.

References Classify(), LogLikelihood(), Probability(), Random(), Serialize(), Train(), and weights.

Member Data Documentation

size_t mlpack::gmm::GMM::dimensionality

private

The dimensionality of the model.

Definition at line 85 of file gmm.hpp.

Referenced by Dimensionality().

std::vector<distribution::GaussianDistribution> mlpack::gmm::GMM::dists

private

Vector of Gaussians.

Definition at line 88 of file gmm.hpp.

size_t mlpack::gmm::GMM::gaussians

private

The number of Gaussians in the model.

Definition at line 83 of file gmm.hpp.

Referenced by Gaussians().

arma::vec mlpack::gmm::GMM::weights

private

Vector of a priori weights for each Gaussian.

Definition at line 91 of file gmm.hpp.

Referenced by Weights().

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

src/mlpack/methods/gmm/gmm.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation