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