wolffd@0: function mix = gmm(dim, ncentres, covar_type, ppca_dim)
wolffd@0: %GMM	Creates a Gaussian mixture model with specified architecture.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	 MIX = GMM(DIM, NCENTRES, COVARTYPE) takes the dimension of the space
wolffd@0: %	DIM, the number of centres in the mixture model and the type of the
wolffd@0: %	mixture model, and returns a data structure MIX. The mixture model
wolffd@0: %	type defines the covariance structure of each component  Gaussian:
wolffd@0: %	  'spherical' = single variance parameter for each component: stored as a vector
wolffd@0: %	  'diag' = diagonal matrix for each component: stored as rows of a matrix
wolffd@0: %	  'full' = full matrix for each component: stored as 3d array
wolffd@0: %	  'ppca' = probabilistic PCA: stored as principal components (in a 3d array
wolffd@0: %	    and associated variances and off-subspace noise
wolffd@0: %	 MIX = GMM(DIM, NCENTRES, COVARTYPE, PPCA_DIM) also sets the
wolffd@0: %	dimension of the PPCA sub-spaces: the default value is one.
wolffd@0: %
wolffd@0: %	The priors are initialised to equal values summing to one, and the
wolffd@0: %	covariances are all the identity matrix (or equivalent).  The centres
wolffd@0: %	are initialised randomly from a zero mean unit variance Gaussian.
wolffd@0: %	This makes use of the MATLAB function RANDN and so the seed for the
wolffd@0: %	random weight initialisation can be set using RANDN('STATE', S) where
wolffd@0: %	S is the state value.
wolffd@0: %
wolffd@0: %	The fields in MIX are
wolffd@0: %	  
wolffd@0: %	  type = 'gmm'
wolffd@0: %	  nin = the dimension of the space
wolffd@0: %	  ncentres = number of mixture components
wolffd@0: %	  covartype = string for type of variance model
wolffd@0: %	  priors = mixing coefficients
wolffd@0: %	  centres = means of Gaussians: stored as rows of a matrix
wolffd@0: %	  covars = covariances of Gaussians
wolffd@0: %	 The additional fields for mixtures of PPCA are
wolffd@0: %	  U = principal component subspaces
wolffd@0: %	  lambda = in-space covariances: stored as rows of a matrix
wolffd@0: %	 The off-subspace noise is stored in COVARS.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	GMMPAK, GMMUNPAK, GMMSAMP, GMMINIT, GMMEM, GMMACTIV, GMMPOST, 
wolffd@0: %	GMMPROB
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: if ncentres < 1
wolffd@0:   error('Number of centres must be greater than zero')
wolffd@0: end
wolffd@0: 
wolffd@0: mix.type = 'gmm';
wolffd@0: mix.nin = dim;
wolffd@0: mix.ncentres = ncentres;
wolffd@0: 
wolffd@0: vartypes = {'spherical', 'diag', 'full', 'ppca'};
wolffd@0: 
wolffd@0: if sum(strcmp(covar_type, vartypes)) == 0
wolffd@0:   error('Undefined covariance type')
wolffd@0: else
wolffd@0:   mix.covar_type = covar_type;
wolffd@0: end
wolffd@0: 
wolffd@0: % Make default dimension of PPCA subspaces one.
wolffd@0: if strcmp(covar_type, 'ppca')
wolffd@0:   if nargin < 4
wolffd@0:     ppca_dim = 1;
wolffd@0:   end
wolffd@0:   if ppca_dim > dim
wolffd@0:     error('Dimension of PPCA subspaces must be less than data.')
wolffd@0:   end
wolffd@0:   mix.ppca_dim = ppca_dim;
wolffd@0: end
wolffd@0: 
wolffd@0: % Initialise priors to be equal and summing to one
wolffd@0: mix.priors = ones(1,mix.ncentres) ./ mix.ncentres;
wolffd@0: 
wolffd@0: % Initialise centres
wolffd@0: mix.centres = randn(mix.ncentres, mix.nin);
wolffd@0: 
wolffd@0: % Initialise all the variances to unity
wolffd@0: switch mix.covar_type
wolffd@0: 
wolffd@0: case 'spherical'
wolffd@0:   mix.covars = ones(1, mix.ncentres);
wolffd@0:   mix.nwts = mix.ncentres + mix.ncentres*mix.nin + mix.ncentres;
wolffd@0: case 'diag'
wolffd@0:   % Store diagonals of covariance matrices as rows in a matrix
wolffd@0:   mix.covars =  ones(mix.ncentres, mix.nin);
wolffd@0:   mix.nwts = mix.ncentres + mix.ncentres*mix.nin + ...
wolffd@0:     mix.ncentres*mix.nin;
wolffd@0: case 'full'
wolffd@0:   % Store covariance matrices in a row vector of matrices
wolffd@0:   mix.covars = repmat(eye(mix.nin), [1 1 mix.ncentres]);
wolffd@0:   mix.nwts = mix.ncentres + mix.ncentres*mix.nin + ...
wolffd@0:     mix.ncentres*mix.nin*mix.nin;
wolffd@0: case 'ppca'
wolffd@0:   % This is the off-subspace noise: make it smaller than
wolffd@0:   % lambdas
wolffd@0:   mix.covars = 0.1*ones(1, mix.ncentres);
wolffd@0:   % Also set aside storage for principal components and
wolffd@0:   % associated variances
wolffd@0:   init_space = eye(mix.nin);
wolffd@0:   init_space = init_space(:, 1:mix.ppca_dim);
wolffd@0:   init_space(mix.ppca_dim+1:mix.nin, :) = ...
wolffd@0:     ones(mix.nin - mix.ppca_dim, mix.ppca_dim);
wolffd@0:   mix.U = repmat(init_space , [1 1 mix.ncentres]);
wolffd@0:   mix.lambda = ones(mix.ncentres, mix.ppca_dim);
wolffd@0:   % Take account of additional parameters
wolffd@0:   mix.nwts = mix.ncentres + mix.ncentres*mix.nin + ...
wolffd@0:     mix.ncentres + mix.ncentres*mix.ppca_dim + ...
wolffd@0:     mix.ncentres*mix.nin*mix.ppca_dim;
wolffd@0: otherwise
wolffd@0:   error(['Unknown covariance type ', mix.covar_type]);               
wolffd@0: end
wolffd@0: