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