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Statistical Learning Toolbox

from Statistical Learning Toolbox by Dahua Lin
Functions for statistical learning, pattern recognition and computer vision, covering many topics.

Description of slgmm
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slgmm

PURPOSE ^

SLGMM Learns Gaussian Mixture model from samples

SYNOPSIS ^

function [GS, pp, info] = slgmm(X, varargin)

DESCRIPTION ^

SLGMM Learns Gaussian Mixture model from samples

 $ Syntax $
   - GS = slgmm(X, ...)
   - [GS, pp] = slgmm(X, ...)
   - [GS, pp, info] = slgmm(X, ...)

 $ Arguments $
   - GS:       The Gaussian model struct with mixture weights
   - pp:       the posteriori of samples to component models
   - info:     the information of learning process
   - X:        the sample matrix 

 $ Description $
   - GS = slgmm(X, ...) learns Gaussian mixture model from samples
     in matrix X. The following properties can be specified:
     \*  
     \t    Table. Properties of Learning Gausssian Mixture Model
     \h    name         &      description                      \\
          'method'      & The method using for GMM learning. Currently,
                          there are only one method available: 'EM',
                          default = 'EM'.
          'K'           & The number of initial components in the mixture 
                          model (default = 3)                     \\
          'update'      & The way of updating (default = 'pass'):
                          1. 'pass'     Pass-wise update;
                          2. 'comp'     Component-wise update     \\
          'cyclecn'     & The ratio of components to be updated in each 
                          cycle for 'comp' update scheme. default = 1.
          'maxiter'     & The maximum number of iterations 
                          (default = 100) \\
          'tol'         & The maximum tolerance of posteriori error when 
                          the iteration terminates, (default = 1e-6) \\
          'verbose'     & whether to display information while iteration, 
                          default = true                              \\
          'annthres'    & The threshold of annealing in FJ algorithm, 
                          default = 0 (unit = average mixture weight) \\
          'weights'     & The weights of the samples, default = [], 
                          indicating non-weighted. Weights should be given
                          by a 1 x n row vector. \\
          'varform'     & The form of variance: 'univar'|'diagvar'|'covar', 
                          default = 'covar';          \\
          'sharevar'    & Whether the variance is shared by all models,
                          default = false;            \\
          'invparams'   & The parameters for computing inverse of variance
                          default = {}                \\
           
 $ Remarks $
   - In current version, the component-wise update scheme is only
     supported when sharevar is false.

 $ History $
   - Created by Dahua Lin, on Aug 28, 2006

CROSS-REFERENCE INFORMATION ^

This function calls:
  • slclassify_eucnn SLCLASSIFY_EUCNN Classifies samples using Euclidena-based NN
  • slfmm SLFMM Learns a Finite Mixture Model (FMM)
  • slgaussest SLGAUSSEST Estimates the Gaussian models from samples
  • slgausspdf SLGAUSSPDF Computes the probability density of Gaussian models
  • slgausstype SLGAUSSTYPE Judges the type of a Gaussian model struct
  • slignorevars SLIGNOREVARS Ignores the input variables
  • slparseprops SLPARSEPROPS Parses input parameters
This function is called by:

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function [GS, pp, info] = slgmm(X, varargin)
0002 %SLGMM Learns Gaussian Mixture model from samples
0003 %
0004 % $ Syntax $
0005 %   - GS = slgmm(X, ...)
0006 %   - [GS, pp] = slgmm(X, ...)
0007 %   - [GS, pp, info] = slgmm(X, ...)
0008 %
0009 % $ Arguments $
0010 %   - GS:       The Gaussian model struct with mixture weights
0011 %   - pp:       the posteriori of samples to component models
0012 %   - info:     the information of learning process
0013 %   - X:        the sample matrix
0014 %
0015 % $ Description $
0016 %   - GS = slgmm(X, ...) learns Gaussian mixture model from samples
0017 %     in matrix X. The following properties can be specified:
0018 %     \*
0019 %     \t    Table. Properties of Learning Gausssian Mixture Model
0020 %     \h    name         &      description                      \\
0021 %          'method'      & The method using for GMM learning. Currently,
0022 %                          there are only one method available: 'EM',
0023 %                          default = 'EM'.
0024 %          'K'           & The number of initial components in the mixture
0025 %                          model (default = 3)                     \\
0026 %          'update'      & The way of updating (default = 'pass'):
0027 %                          1. 'pass'     Pass-wise update;
0028 %                          2. 'comp'     Component-wise update     \\
0029 %          'cyclecn'     & The ratio of components to be updated in each
0030 %                          cycle for 'comp' update scheme. default = 1.
0031 %          'maxiter'     & The maximum number of iterations
0032 %                          (default = 100) \\
0033 %          'tol'         & The maximum tolerance of posteriori error when
0034 %                          the iteration terminates, (default = 1e-6) \\
0035 %          'verbose'     & whether to display information while iteration,
0036 %                          default = true                              \\
0037 %          'annthres'    & The threshold of annealing in FJ algorithm,
0038 %                          default = 0 (unit = average mixture weight) \\
0039 %          'weights'     & The weights of the samples, default = [],
0040 %                          indicating non-weighted. Weights should be given
0041 %                          by a 1 x n row vector. \\
0042 %          'varform'     & The form of variance: 'univar'|'diagvar'|'covar',
0043 %                          default = 'covar';          \\
0044 %          'sharevar'    & Whether the variance is shared by all models,
0045 %                          default = false;            \\
0046 %          'invparams'   & The parameters for computing inverse of variance
0047 %                          default = {}                \\
0048 %
0049 % $ Remarks $
0050 %   - In current version, the component-wise update scheme is only
0051 %     supported when sharevar is false.
0052 %
0053 % $ History $
0054 %   - Created by Dahua Lin, on Aug 28, 2006
0055 %
0056 
0057 %% parse and verify input arguments
0058 
0059 if ~isnumeric(X) || ndims(X) ~= 2
0060     error('sltoolbox:invalidarg', ...
0061         'X should be a 2D numeric matrix');
0062 end
0063 
0064 opts.method = 'EM';
0065 opts.K = 3;
0066 opts.update = 'pass';
0067 opts.cyclecn = 1;
0068 opts.maxiter = 100;
0069 opts.tol = 1e-6;
0070 opts.verbose = true;
0071 opts.annthres = 0;
0072 opts.weights = [];
0073 opts.varform = 'covar';
0074 opts.sharevar = false;
0075 opts.invparams = {};
0076 opts = slparseprops(opts, varargin{:});
0077 
0078 n = size(X, 2);
0079 
0080 
0081 %% initialization by random clustering
0082 
0083 if opts.K > n
0084     error('sltoolbox:sizoverflow', ...
0085         'The K is larger than the number of samples');
0086 end
0087 
0088 init_centerinds = randsample(n, opts.K);
0089 init_centers = X(:, init_centerinds);
0090 initc = slclassify_eucnn(init_centers, X);
0091 
0092 %% perform learning based on FMM
0093 
0094 estfunctor = {@gmm_estfunc, opts.varform, opts.sharevar, opts.invparams};
0095 evalfunctor = {@gmm_evalfunc};
0096 
0097 [GS, cw, pp, info] = slfmm(X, n, estfunctor, evalfunctor, ...
0098     'method', opts.method, ...
0099     'update', opts.update, ...
0100     'cyclecn', opts.cyclecn, ...
0101     'iter', {'maxiter', opts.maxiter}, ...
0102     'tol', opts.tol, ...
0103     'verbose', opts.verbose, ...
0104     'initc', initc, ...
0105     'annthres', opts.annthres, ...
0106     'weights', opts.weights, ...
0107     'estmode', 'innermul', ...
0108     'condpmode', 'log', ...
0109     'manifunc', @gmm_manifunc);
0110 
0111 %% post actions
0112 
0113 GS.mixweights = cw;
0114 
0115 
0116 %% Core slot functions
0117 
0118 function GS = gmm_estfunc(GS, X, n, W, selinds, varform, sharevar, invparams)
0119 
0120 slignorevars(n);
0121 
0122 if isempty(selinds)
0123     GS = slgaussest(X, 'weights', W, ...
0124         'varform', varform, 'sharevar', sharevar, ...
0125         'compinv', true, 'invparams', invparams);
0126 else
0127     if sharevar
0128         error('sltoolbox:rterror', ...
0129             'The selective updating scheme is only supported when sharevar is false');
0130     end
0131     
0132     Wsel = W(selinds, :);
0133     GSu = slgaussest(X, 'weights', Wsel, ...
0134         'varform', varform, 'sharevar', sharevar, ...
0135         'compinv', true, 'invparams', invparams);
0136     
0137     nu = length(selinds);
0138     switch varform
0139         case 'univar'
0140             for idx = 1 : nu
0141                 iu = selinds(idx);
0142                 GS.means(:, iu) = GSu.means(:,idx);
0143                 GS.vars(iu) = GSu.vars(idx);
0144                 GS.invvars(iu) = GSu.invvars(idx);
0145             end
0146         case 'diagvar'
0147             for idx = 1 : nu
0148                 iu = selinds(idx);
0149                 GS.means(:, iu) = GSu.means(:, idx);
0150                 GS.vars(:, iu) = GSu.vars(:, idx);
0151                 GS.invvars(:, iu) = GSu.invvars(:, idx);
0152             end
0153         case 'covar'
0154             for idx = 1 : nu
0155                 iu = selinds(idx);
0156                 GS.means(:, iu) = GSu.means(:, idx);
0157                 GS.covs(:,:, iu) = GSu.covs(:,:, idx);
0158                 GS.invcovs(:,:, iu) = GSu.invcovs(:,:, idx);
0159             end
0160     end
0161     
0162 end
0163 
0164 function condp = gmm_evalfunc(GS, X, n)
0165 
0166 slignorevars(n);
0167 condp = slgausspdf(GS, X, 'output', 'log');
0168 
0169 
0170 function GS = gmm_manifunc(GS0, op, varargin)
0171 
0172 switch op
0173     case 'select'
0174         
0175         selinds = varargin{1};
0176         
0177         tyi = slgausstype(GS0);
0178         
0179         GS.dim = GS0.dim;
0180         GS.nmodels = length(selinds);
0181         GS.means = GS0.means(:, selinds);
0182         
0183         switch tyi.varform
0184             case {'univar', 'diagvar'}
0185                 if tyi.sharevar
0186                     GS.vars = GS0.vars;
0187                     GS.invvars = GS0.invvars;
0188                 else
0189                     GS.vars = GS0.vars(:, selinds);
0190                     GS.invvars = GS0.invvars(:, selinds);
0191                 end
0192             case 'covar'
0193                 if tyi.sharevar
0194                     GS.covs = GS0.covs;
0195                     GS.invcovs = GS0.invcovs;
0196                 else
0197                     GS.covs = GS0.covs(:,:,selinds);
0198                     GS.invcovs = GS0.invcovs(:,:,selinds);
0199                 end
0200         end
0201         
0202         
0203     otherwise
0204         error('sltoolbox:invalidarg', ...
0205             'Unsupported manipulation option for GMM: %s', op);
0206 end
0207 
0208 
0209 
0210 
0211 
0212 
0213
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