A k-by-d matrix holding the mean of each of the k components, one per row, where d is the number of variables. This property is read-only.

The covariances of the components, in the form they were given in. A full covariance per component is d-by-d-by-k, a diagonal one per component 1-by-d-by-k, a full covariance shared by every component d-by-d, and a shared diagonal one 1-by-d. This property is read-only.

A 1-by-k row vector holding the proportion of each component. The proportions are scaled to sum to 1, and are all equal when none was given. This property is read-only.

The character vector 'gaussian mixture distribution'. This property is read-only.

A positive integer, the number of rows of mu. This property is read-only.

A positive integer, the dimension of each component, which is the number of columns of mu. This property is read-only.

A character vector, 'diagonal' when each covariance was given as a row of variances and 'full' when it was given as a matrix. This property is read-only.

A logical scalar, true when a single covariance was given for every component and false when one was given per component. This property is read-only.

A scalar, twice the negative log-likelihood plus twice the number of estimated parameters. It is empty unless the object came from fitgmdist. This property is read-only.

A scalar, twice the negative log-likelihood plus the number of estimated parameters times the log of the number of observations. It is empty unless the object came from fitgmdist. This property is read-only.

A logical scalar, true when the fit reached its tolerance within the iteration limit. It is empty unless the object came from fitgmdist. This property is read-only.

A scalar, the negative of the log-likelihood of the data under the fitted mixture. It is empty unless the object came from fitgmdist. This property is read-only.

A positive integer. It is empty unless the object came from fitgmdist. This property is read-only.

A nonnegative scalar added to the diagonal of each covariance to keep it positive definite. It is empty unless the object came from fitgmdist. This property is read-only.

gmdistribution: obj = gmdistribution (mu, Sigma)

gmdistribution: obj = gmdistribution (mu, Sigma, p)

gmdistribution: obj = gmdistribution (mu, Sigma, p, extra)

mu is a k-by-d matrix holding the mean of each of the k components, one per row, where d is the number of variables.

Sigma holds the covariances in one of four forms. A full covariance per component is d-by-d-by-k and a diagonal one per component is 1-by-d-by-k, while a single d-by-d matrix or a single 1-by-d row of variances is shared by every component. The form given sets CovarianceType and SharedCovariance.

p is a vector of k mixing proportions, scaled to sum to 1. A proportion may not be negative and they may not all be zero. When p is omitted or empty the components are equally weighted.

extra carries the results of a fit and is passed by fitgmdist. It fills AIC, BIC, Converged, NegativeLogLikelihood, NumIterations and RegularizationValue, which stay empty for an object built by hand.

gmdistribution: c = cdf (obj, X)

X is an n-by-d matrix of points at which the distribution is evaluated, one point per row, where d is the number of variables of obj. c is an n-by-1 vector holding the value of the cumulative distribution function at each of them, the components’ cumulative distributions summed with the mixing proportions in ComponentProportion as weights.

gmdistribution: idx = cluster (obj, X)

gmdistribution: [idx, nlogl] = cluster (obj, X)

gmdistribution: [idx, nlogl, P] = cluster (obj, X)

gmdistribution: [idx, nlogl, P, logpdf] = cluster (obj, X)

gmdistribution: [idx, nlogl, P, logpdf, M] = cluster (obj, X)

X is an n-by-d matrix of observations, one per row, where d is the number of variables of obj. Each is assigned to the component under which it is most probable.

idx is an n-by-1 vector of component indices. nlogl is the negative log-likelihood of X under the mixture. P is an n-by-k matrix of posterior probabilities, one column per component, whose rows sum to one. logpdf is an n-by-1 vector holding the logarithm of the mixture density at each observation. M is an n-by-k matrix of squared Mahalanobis distances from each observation to each component mean.

gmdistribution: D = mahal (obj, X)

X is an n-by-d matrix of observations, one per row, where d is the number of variables of obj. D is an n-by-k matrix holding the squared Mahalanobis distance from each observation to the mean of each of the k components, measured in the covariance of the component it is taken to.

gmdistribution: c = pdf (obj, X)

X is an n-by-d matrix of points at which the density is evaluated, one point per row, where d is the number of variables of obj. c is an n-by-1 vector holding the density at each of them, the components’ densities summed with the mixing proportions in ComponentProportion as weights.

gmdistribution: c = posterior (obj, X)

X is an n-by-d matrix of observations, one per row, where d is the number of variables of obj. c is an n-by-k matrix whose (i,j) element is the probability that observation i was drawn from component j, so its rows sum to one.

gmdistribution: c = random (obj)

gmdistribution: c = random (obj, n)

n is the number of observations to draw and defaults to 1. c is an n-by-d matrix holding one observation per row, where d is the number of variables of obj. Each row is drawn from a component chosen with probability ComponentProportion.

gmdistribution: obj = fit (X, k)

gmdistribution: obj = fit (X, k, Name, Value)

X is an n-by-d matrix of observations, one per row, and k is the number of components to fit. Any Name-Value pair accepted by fitgmdist may follow, which is the function this method calls and where the options are documented. obj is the fitted gmdistribution object.