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Gaussian mixture models

An object of the `gmdistribution`

class defines
a Gaussian mixture distribution, which is a multivariate distribution
that consists of a mixture of one or more multivariate Gaussian distribution
components. The number of components for a given `gmdistribution`

object
is fixed. Each multivariate Gaussian component is defined by its
mean and covariance, and the mixture is defined by a vector of mixing
proportions.

To create a Gaussian mixture distribution by specifying the
distribution parameters, use the `gmdistribution`

constructor.
To fit a Gaussian mixture distribution model to data, use `fitgmdist`

.

fit | Gaussian mixture parameter estimates |

gmdistribution | Construct Gaussian mixture distribution |

All objects of the class have the properties listed in the following table.

ComponentProportion | Input vector of mixing proportions |

CovarianceType | Type of covariance matrices |

DistributionName | Type of distribution |

mu | Input matrix of means `mu` |

NumComponents | Number k of mixture components |

NumVariables | Dimension d of multivariate Gaussian
distributions |

ProbabilityTolerance | Tolerance for posterior probabilities |

SharedCovariance | `true` if all covariance matrices are
restricted to be the same |

Sigma | Input array of covariances |

Objects constructed with `fitgmdist`

have
the additional properties listed in the following table.

AIC | Akaike Information Criterion |

BIC | Bayes Information Criterion |

Converged | Determine if algorithm converged |

NegativeLogLikelihood | Negative of log-likelihood |

NumIterations | Number of iterations |

RegularizationValue | Value of `'Regularize'` parameter |

cdf | Cumulative distribution function for Gaussian mixture distribution |

cluster | Construct clusters from Gaussian mixture distribution |

disp | Display Gaussian mixture distribution object |

display | Display Gaussian mixture distribution object |

fit | Gaussian mixture parameter estimates |

mahal | Mahalanobis distance to component means |

Probability density function for Gaussian mixture distribution | |

posterior | Posterior probabilities of components |

random | Random numbers from Gaussian mixture distribution |

subsasgn | Subscripted reference for Gaussian mixture distribution object |

subsref | Subscripted reference for Gaussian mixture distribution object |

Value. To learn how value classes affect
copy operations, see Copying Objects in
the MATLAB^{®} documentation.

[1] McLachlan, G., and D. Peel. *Finite
Mixture Models*. Hoboken, NJ: John Wiley & Sons, Inc.,
2000.

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