# rbf

## Purpose

Creates an RBF network with specified architecture

## Synopsis

    net = rbf(nin, nhidden, nout, rbfunc)
    net = rbf(nin, nhidden, nout, rbfunc, outfunc)
    net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)

## Description

`net = rbf(nin, nhidden, nout, rbfunc)` constructs and initialises a radial basis function network returning a data structure `net`. 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 `randn` and so the seed for the random weight initialization can be set using `randn('state', s)` where `s` 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.)

The fields in `net` are

      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

`net = rbf(nin, nhidden, nout, rbfund, outfunc)` allows the user to specify the type of error function to be used. The field `outfn` is set to the value of this string. Linear outputs (for regression problems) and Neuroscale outputs (for topographic mappings) are supported.

`net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)`, in which `prior` is a scalar, allows the field `net.alpha` in the data structure `net` to be set, corresponding to a zero-mean isotropic Gaussian prior with inverse variance with value `prior`. Alternatively, `prior` can consist of a data structure with fields `alpha` and `index`, allowing individual Gaussian priors to be set over groups of weights in the network. Here `alpha` 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 `indx` in which the columns correspond to the elements of `alpha`. Each column has one element for each weight in the matrix, in the order defined by the function `rbfpak`, and each element is 1 or 0 according to whether the weight is a member of the corresponding group or not. A utility function `rbfprior` is provided to help in setting up the `prior` data structure.

`net = rbf(nin, nhidden, nout, func, prior, beta)` also sets the additional field `net.beta` in the data structure `net`, where beta corresponds to the inverse noise variance.

## Example

The following code constructs an RBF network with 1 input and output node and 5 hidden nodes and then propagates some data `x` through it.

    net = rbf(1, 5, 1, 'tps');
    [y, act] = rbffwd(net, x);

## See Also

`rbferr`, `rbffwd`, `rbfgrad`, `rbfpak`, `rbftrain`, `rbfunpak`

Pages: Index

Copyright (c) Ian T Nabney (1996-9)