matlab gmdistribution.fit,gmdistribution.fit使用

link:http://www.mbfys.ru.nl/~robvdw/CNP04/LAB_ASSIGMENTS/LAB05_CN05/MATLAB2007b

/stats/@gmdistribution/fit.m源文件

%FIT Fit data to Gaussian mixture model

% G = GMDISTRIBUTION.FIT(X,K) creates an object G containing maximum

% likelihood estimates of the parameters in a Gaussian mixture model with

% K components for the data in X. X is an N-by-D matrix. Rows of X

% correspond to points; columns correspond to variables. The

% estimation uses the Expectation Maximization (EM) algorithm.

%

% GMDISTRIBUTION treats NaNs as missing data. Rows of X with NaNs are

% excluded from the fit.

%

% G = GMDISTRIBUTION.FIT(...,'PARAM1',val1,'PARAM2',val2,...)

% provides more control over the iterative EM algorithm. Parameters

% and values are listed below.

%

% 'Start' Method used to choose initial component parameters.

% There are three choices:

%

% 'randSample' Select K observations from X at random as the

% initial component means. The mixing

% proportions are uniform. The initial

% covariance matrices for all clusters are

% diagonal, where the Jth element on the diagonal

% is the variance of X(:,J). This is the default.

%

% A structure array S containing the following fields:

%

% S.PComponents:

% A 1-by-K vector specifying the mixing

% proportions of each component. The default

% is uniform.

%

% S.mu:

% A K-by-D matrix specifying the mean of each

% component.

%

% S.Sigma:

% An array specifying the covariance of each

% component. The size of Sigma is one of the

% following:

% * D-by-D-by-K array if there are no

% restrictions on the form of covariance. In

% this case, S.Sigma(:,:,J) is the covariance

% of component J.

% * 1-by-D-by-K array if the covariance matrices

% are restricted to be diagonal, but not

% restricted to be same across components. In

% this case, S.Sigma(:,:,J) contains the

% diagonal elements of the covariance of

% component J.

% * D-by-D matrix if the covariance matrices are

% restricted to be the same across clusters,

% but not restricted to be diagonal. In this

% case, S.Sigma is the pooled estimate of

% covariance.

% * 1-by-D vector if the covariance matrices are

% restricted to be diagonal and to be the same

% across clusters. In this case, S.Sigma

% contains the diagonal elements of the pooled

% estimate of covariance.

%

% A vector of length N containing the initial guess of the

% component index for each point.

%

% 'Replicates' A positive integer giving the number of times to

% repeat the EM algorithm, each with a new set of

% parameters. The solution with the largest likelihood

% is returned. The default number of replicates is 1.

% A value larger than 1 requires the 'randSample'

% start method.

%

% 'CovType' 'diagonal' if the covariance matrices are restricted to

% be diagonal; 'full' otherwise. The default is 'full'.

%

% 'SharedCov' True if all the covariance matrices are restricted to be

% the same (pooled estimate); false otherwise. The default

% is false.

%

% 'Regularize' A non-negative regularization number added to the

% diagonal of covariance matrices to make them positive-

% definite. The default is 0.

%

% 'Options' Options structure for the iterative EM algorithm, as

% created by STATSET. The following STATSET parameters

% are used:

%

% 'Display' Level of display output. Choices are

% 'off' (the default), 'final', and 'iter'.

% 'MaxIter' Maximum number of iterations allowed.

% Default is 100.

% 'TolFun' Positive number giving the termination

% tolerance for the log-likelihood

% function. The default is 1e-6.

%

% The properties of the object G are listed below.

% G.NDimensions The dimension of multivariate Gaussian distribution.

% It equals D.

% G.DistName The name of distribution. In gmdistribution, it is

% 'gaussian mixture distribution'

% G.NComponents The number of mixture components K.

% G.PComponents A 1-by-K vector containing the mixing proportion of

% each component.

% G.mu A K-by-D array of means.

% G.Sigma An array or a matrix containing the covariance of

% each component. The size of Sigma is:

% * D-by-D-by-K array if there are no restrictions on

% the form of covariance. In this case,

% G.Sigma(:,:,j) is the covariance of component j.

% * 1-by-D-by-K array if the covariance matrices are

% restricted to be diagonal, but not restricted to

% be same across components. In this case

% G.Sigma(:,:,j) contains the diagonal elements of

% the covariance of component j.

% * D-by-D matrix if the covariance matrices are

% restricted to be the same across clusters, but not

% restricted to be diagonal. In this case, G.Sigma

% is the pooled estimate of covariance.

% * 1-by-D vector if the covariance matrices are

% restricted to be diagonal and to be the same

% across clusters. In this case, G.Sigma contains

% the diagonal elements of the pooled estimate of

% covariance.

% G.NlogL The negative of the log-likelihood of the data.

% G.AIC The Akaike information criterion, which is

% 2*NlogL + 2*the number of estimated parameters.

% G.BIC The Bayes information criterion, which is

% 2*NlogL + (the number of estimated parameters *

% log(N)).

% G.Converged True if the algorithm has converged; false if the

% algorithm has not converged.

% G.Iters The number of iterations of the algorithm.

% G.CovType The value of the 'CovType' input parameter.

% G.SharedCov The value of the 'SharedCov' input parameter.

% G.RegV The value of the 'Regularize' input parameter.

%

% Example: Generate data from a mixture of two bivariate Gaussian

% distributions and fit a Gaussian mixture model:

% mu1 = [1 2];

% Sigma1 = [2 0; 0 .5];

% mu2 = [-3 -5];

% Sigma2 = [1 0; 0 1];

% X = [mvnrnd(mu1,Sigma1,1000);mvnrnd(mu2,Sigma2,1000)];

% G = gmdistribution.fit(X,2);

%

% See also GMDISTRIBUTION, GMDISTRIBUTION/CLUSTER, KMEANS.

% Reference: McLachlan, G., and D. Peel, Finite Mixture Models, John

% Wiley & Sons, New York, 2000.

% Copyright 2007 The MathWorks, Inc.

% $Revision: 1.1.6.1 $ $Date: 2007/06/14 05:26:19 $