Daniel@0: Daniel@0: Daniel@0: Daniel@0: Netlab Reference Manual gmm Daniel@0: Daniel@0: Daniel@0: Daniel@0:

gmm Daniel@0:

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Daniel@0: Purpose Daniel@0:

Daniel@0: Creates a Gaussian mixture model with specified architecture. Daniel@0: Daniel@0:

Daniel@0: Synopsis Daniel@0:

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Daniel@0: mix = gmm(dim, ncentres, covartype)
Daniel@0: mix = gmm(dim, ncentres, covartype, ppca_dim)
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Daniel@0: Daniel@0: Daniel@0:

Daniel@0: Description Daniel@0:

Daniel@0: Daniel@0: mix = gmm(dim, ncentres, covartype) takes Daniel@0: the dimension of the space dim, the number of centres in the Daniel@0: mixture model and the type of the mixture model, and returns a data Daniel@0: structure mix. Daniel@0: The mixture model type defines the covariance structure of each component Daniel@0: Gaussian: Daniel@0:

Daniel@0: 
Daniel@0:   'spherical' = single variance parameter for each component: stored as a vector
Daniel@0:   'diag' = diagonal matrix for each component: stored as rows of a matrix
Daniel@0:   'full' = full matrix for each component: stored as 3d array
Daniel@0:   'ppca' = probabilistic PCA: stored as principal components (in a 3d array
Daniel@0:     and associated variances and off-subspace noise
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Daniel@0: Daniel@0: mix = gmm(dim, ncentres, covartype, ppca_dim) also sets the dimension of Daniel@0: the PPCA sub-spaces: the default value is one. Daniel@0: Daniel@0:

The priors are initialised to equal values summing to one, and the covariances Daniel@0: are all the identity matrix (or equivalent). The centres are Daniel@0: initialised randomly from a zero mean unit variance Gaussian. This makes use Daniel@0: of the MATLAB function randn and so the seed for the random weight Daniel@0: initialisation can be set using randn('state', s) where s is the Daniel@0: state value. Daniel@0: Daniel@0:

The fields in mix are Daniel@0:

Daniel@0:   
Daniel@0:   type = 'gmm'
Daniel@0:   nin = the dimension of the space
Daniel@0:   ncentres = number of mixture components
Daniel@0:   covartype = string for type of variance model
Daniel@0:   priors = mixing coefficients
Daniel@0:   centres = means of Gaussians: stored as rows of a matrix
Daniel@0:   covars = covariances of Gaussians
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Daniel@0: Daniel@0: The additional fields for mixtures of PPCA are Daniel@0:

Daniel@0: 
Daniel@0:   U = principal component subspaces
Daniel@0:   lambda = in-space covariances: stored as rows of a matrix
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Daniel@0: Daniel@0: The off-subspace noise is stored in covars. Daniel@0: Daniel@0:

Daniel@0: Example Daniel@0:

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Daniel@0: 
Daniel@0: mix = gmm(2, 4, 'spherical');
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Daniel@0: Daniel@0: This creates a Gaussian mixture model with 4 components in 2 dimensions. Daniel@0: The covariance structure is a spherical model. Daniel@0: Daniel@0:

Daniel@0: See Also Daniel@0:

Daniel@0: gmmpak, gmmunpak, gmmsamp, gmminit, gmmem, gmmactiv, gmmpost, gmmprob

Daniel@0: Pages: Daniel@0: Index Daniel@0:

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