%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 $