mlpack::gmm(3) Gaussian Mixture Models.

SYNOPSIS


Classes


class DiagonalConstraint
Force a covariance matrix to be diagonal.
class EigenvalueRatioConstraint
Given a vector of eigenvalue ratios, ensure that the covariance matrix always has those eigenvalue ratios.
class EMFit
This class contains methods which can fit a GMM to observations using the EM algorithm.
class GMM
A Gaussian Mixture Model (GMM).
class NoConstraint
This class enforces no constraint on the covariance matrix.
class PositiveDefiniteConstraint
Given a covariance matrix, force the matrix to be positive definite.

Functions


double phi (const double x, const double mean, const double var)
Calculates the univariate Gaussian probability density function.
double phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov)
Calculates the multivariate Gaussian probability density function.
double phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov, const std::vector< arma::mat > &d_cov, arma::vec &g_mean, arma::vec &g_cov)
Calculates the multivariate Gaussian probability density function and also the gradients with respect to the mean and the variance.
void phi (const arma::mat &x, const arma::vec &mean, const arma::mat &cov, arma::vec &probabilities)
Calculates the multivariate Gaussian probability density function for each data point (column) in the given matrix, with respect to the given mean and variance.

Detailed Description

Gaussian Mixture Models.

Function Documentation

double mlpack::gmm::phi (const doublex, const doublemean, const doublevar) [inline]

Calculates the univariate Gaussian probability density function. Example use: 

double x, mean, var;
....
double f = phi(x, mean, var);

Parameters:

x Observation.
mean Mean of univariate Gaussian.
var Variance of univariate Gaussian.

Returns:

Probability of x being observed from the given univariate Gaussian.

Definition at line 46 of file phi.hpp.

References M_PI.

Referenced by mlpack::distribution::GaussianDistribution::Probability().

double mlpack::gmm::phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov) [inline]

Calculates the multivariate Gaussian probability density function. Example use: 

extern arma::vec x, mean;
extern arma::mat cov;
....
double f = phi(x, mean, cov);

Parameters:

x Observation.
mean Mean of multivariate Gaussian.
cov Covariance of multivariate Gaussian.

Returns:

Probability of x being observed from the given multivariate Gaussian.

Definition at line 68 of file phi.hpp.

References M_PI.

double mlpack::gmm::phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov, const std::vector< arma::mat > &d_cov, arma::vec &g_mean, arma::vec &g_cov) [inline]

Calculates the multivariate Gaussian probability density function and also the gradients with respect to the mean and the variance. Example use: 

extern arma::vec x, mean, g_mean, g_cov;
std::vector<arma::mat> d_cov; // the dSigma
....
double f = phi(x, mean, cov, d_cov, &g_mean, &g_cov);


 

Definition at line 94 of file phi.hpp.

References M_PI.

void mlpack::gmm::phi (const arma::mat &x, const arma::vec &mean, const arma::mat &cov, arma::vec &probabilities) [inline]

Calculates the multivariate Gaussian probability density function for each data point (column) in the given matrix, with respect to the given mean and variance.

Parameters:

x List of observations.
mean Mean of multivariate Gaussian.
cov Covariance of multivariate Gaussian.
probabilities Output probabilities for each input observation.

Definition at line 138 of file phi.hpp.

References M_PI.

Author

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