mlpack::gmm(3) Gaussian Mixture Models.

## 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.

## 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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