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1 <html>
2 <head>
3 <title>
4 Netlab Reference Manual rbf
5 </title>
6 </head>
7 <body>
8 <H1> rbf
9 </H1>
10 <h2>
11 Purpose
12 </h2>
13 Creates an RBF network with specified architecture
14
15 <p><h2>
16 Synopsis
17 </h2>
18 <PRE>
19
20 net = rbf(nin, nhidden, nout, rbfunc)
21 net = rbf(nin, nhidden, nout, rbfunc, outfunc)
22 net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)
23 </PRE>
24
25
26 <p><h2>
27 Description
28 </h2>
29 <CODE>net = rbf(nin, nhidden, nout, rbfunc)</CODE> constructs and initialises
30 a radial basis function network returning a data structure <CODE>net</CODE>.
31 The weights are all initialised with a zero mean, unit variance normal
32 distribution, with the exception of the variances, which are set to one.
33 This makes use of the Matlab function
34 <CODE>randn</CODE> and so the seed for the random weight initialization can be
35 set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the seed value. The
36 activation functions are defined in terms of the distance between
37 the data point and the corresponding centre. Note that the functions are
38 computed to a convenient constant multiple: for example, the Gaussian
39 is not normalised. (Normalisation is not needed as the function outputs
40 are linearly combined in the next layer.)
41
42 <p>The fields in <CODE>net</CODE> are
43 <PRE>
44
45 type = 'rbf'
46 nin = number of inputs
47 nhidden = number of hidden units
48 nout = number of outputs
49 nwts = total number of weights and biases
50 actfn = string defining hidden unit activation function:
51 'gaussian' for a radially symmetric Gaussian function.
52 'tps' for r^2 log r, the thin plate spline function.
53 'r4logr' for r^4 log r.
54 outfn = string defining output error function:
55 'linear' for linear outputs (default) and SoS error.
56 'neuroscale' for Sammon stress measure.
57 c = centres
58 wi = squared widths (null for rlogr and tps)
59 w2 = second layer weight matrix
60 b2 = second layer bias vector
61 </PRE>
62
63
64 <p><CODE>net = rbf(nin, nhidden, nout, rbfund, outfunc)</CODE> allows the user to
65 specify the type of error function to be used. The field <CODE>outfn</CODE>
66 is set to the value of this string. Linear outputs (for regression problems)
67 and Neuroscale outputs (for topographic mappings) are supported.
68
69 <p><CODE>net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)</CODE>,
70 in which <CODE>prior</CODE> is
71 a scalar, allows the field <CODE>net.alpha</CODE> in the data structure
72 <CODE>net</CODE> to be set, corresponding to a zero-mean isotropic Gaussian
73 prior with inverse variance with value <CODE>prior</CODE>. Alternatively,
74 <CODE>prior</CODE> can consist of a data structure with fields <CODE>alpha</CODE>
75 and <CODE>index</CODE>, allowing individual Gaussian priors to be set over
76 groups of weights in the network. Here <CODE>alpha</CODE> is a column vector
77 in which each element corresponds to a separate group of weights,
78 which need not be mutually exclusive. The membership of the groups is
79 defined by the matrix <CODE>indx</CODE> in which the columns correspond to
80 the elements of <CODE>alpha</CODE>. Each column has one element for each
81 weight in the matrix, in the order defined by the function
82 <CODE>rbfpak</CODE>, and each element is 1 or 0 according to whether the
83 weight is a member of the corresponding group or not. A utility
84 function <CODE>rbfprior</CODE> is provided to help in setting up the
85 <CODE>prior</CODE> data structure.
86
87 <p><CODE>net = rbf(nin, nhidden, nout, func, prior, beta)</CODE> also sets the
88 additional field <CODE>net.beta</CODE> in the data structure <CODE>net</CODE>, where
89 beta corresponds to the inverse noise variance.
90
91 <p><h2>
92 Example
93 </h2>
94 The following code constructs an RBF network with 1 input and output node
95 and 5 hidden nodes and then propagates some data <CODE>x</CODE> through it.
96 <PRE>
97
98 net = rbf(1, 5, 1, 'tps');
99 [y, act] = rbffwd(net, x);
100 </PRE>
101
102
103 <p><h2>
104 See Also
105 </h2>
106 <CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE><hr>
107 <b>Pages:</b>
108 <a href="index.htm">Index</a>
109 <hr>
110 <p>Copyright (c) Ian T Nabney (1996-9)
111
112
113 </body>
114 </html>