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1 <html>
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2 <head>
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3 <title>
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4 Netlab Reference Manual gmm
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5 </title>
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6 </head>
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7 <body>
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8 <H1> gmm
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9 </H1>
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10 <h2>
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11 Purpose
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12 </h2>
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13 Creates a Gaussian mixture model with specified architecture.
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14
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15 <p><h2>
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16 Synopsis
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17 </h2>
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18 <PRE>
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19 mix = gmm(dim, ncentres, covartype)
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20 mix = gmm(dim, ncentres, covartype, ppca_dim)
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21 </PRE>
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22
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23
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24 <p><h2>
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25 Description
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26 </h2>
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27
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28 <CODE>mix = gmm(dim, ncentres, covartype)</CODE> takes
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29 the dimension of the space <CODE>dim</CODE>, the number of centres in the
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30 mixture model and the type of the mixture model, and returns a data
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31 structure <CODE>mix</CODE>.
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32 The mixture model type defines the covariance structure of each component
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33 Gaussian:
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34 <PRE>
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35
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36 'spherical' = single variance parameter for each component: stored as a vector
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37 'diag' = diagonal matrix for each component: stored as rows of a matrix
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38 'full' = full matrix for each component: stored as 3d array
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39 'ppca' = probabilistic PCA: stored as principal components (in a 3d array
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40 and associated variances and off-subspace noise
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41 </PRE>
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42
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43 <CODE>mix = gmm(dim, ncentres, covartype, ppca_dim)</CODE> also sets the dimension of
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44 the PPCA sub-spaces: the default value is one.
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45
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46 <p>The priors are initialised to equal values summing to one, and the covariances
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47 are all the identity matrix (or equivalent). The centres are
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48 initialised randomly from a zero mean unit variance Gaussian. This makes use
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49 of the MATLAB function <CODE>randn</CODE> and so the seed for the random weight
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50 initialisation can be set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the
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51 state value.
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52
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53 <p>The fields in <CODE>mix</CODE> are
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54 <PRE>
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55
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56 type = 'gmm'
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57 nin = the dimension of the space
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58 ncentres = number of mixture components
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59 covartype = string for type of variance model
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60 priors = mixing coefficients
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61 centres = means of Gaussians: stored as rows of a matrix
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62 covars = covariances of Gaussians
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63 </PRE>
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64
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65 The additional fields for mixtures of PPCA are
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66 <PRE>
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67
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68 U = principal component subspaces
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69 lambda = in-space covariances: stored as rows of a matrix
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70 </PRE>
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71
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72 The off-subspace noise is stored in <CODE>covars</CODE>.
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73
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74 <p><h2>
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75 Example
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76 </h2>
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77 <PRE>
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78
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79 mix = gmm(2, 4, 'spherical');
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80 </PRE>
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81
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82 This creates a Gaussian mixture model with 4 components in 2 dimensions.
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83 The covariance structure is a spherical model.
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84
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85 <p><h2>
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86 See Also
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87 </h2>
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88 <CODE><a href="gmmpak.htm">gmmpak</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE>, <CODE><a href="gmmsamp.htm">gmmsamp</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmactiv.htm">gmmactiv</a></CODE>, <CODE><a href="gmmpost.htm">gmmpost</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE><hr>
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89 <b>Pages:</b>
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90 <a href="index.htm">Index</a>
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91 <hr>
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92 <p>Copyright (c) Ian T Nabney (1996-9)
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93
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94
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95 </body>
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96 </html> |
