rbf: Create and train a radial basis function (RBF) network

In RSNNS: Neural Networks using the Stuttgart Neural Network Simulator (SNNS)

Create and train a radial basis function (RBF) network

Description

The use of an RBF network is similar to that of an mlp. The idea of radial basis function networks comes from function interpolation theory. The RBF performs a linear combination of n basis functions that are radially symmetric around a center/prototype.

Usage

rbf(x, ...)

## Default S3 method:
rbf(
  x,
  y,
  size = c(5),
  maxit = 100,
  initFunc = "RBF_Weights",
  initFuncParams = c(0, 1, 0, 0.02, 0.04),
  learnFunc = "RadialBasisLearning",
  learnFuncParams = c(1e-05, 0, 1e-05, 0.1, 0.8),
  updateFunc = "Topological_Order",
  updateFuncParams = c(0),
  shufflePatterns = TRUE,
  linOut = TRUE,
  inputsTest = NULL,
  targetsTest = NULL,
  ...
)

Arguments

x	a matrix with training inputs for the network
...	additional function parameters (currently not used)
y	the corresponding targets values
size	number of units in the hidden layer(s)
maxit	maximum of iterations to learn
initFunc	the initialization function to use
initFuncParams	the parameters for the initialization function
learnFunc	the learning function to use
learnFuncParams	the parameters for the learning function
updateFunc	the update function to use
updateFuncParams	the parameters for the update function
shufflePatterns	should the patterns be shuffled?
linOut	sets the activation function of the output units to linear or logistic
inputsTest	a matrix with inputs to test the network
targetsTest	the corresponding targets for the test input

Details

RBF networks are feed-forward networks with one hidden layer. Their activation is not sigmoid (as in MLP), but radially symmetric (often gaussian). Thereby, information is represented locally in the network (in contrast to MLP, where it is globally represented). Advantages of RBF networks in comparison to MLPs are mainly, that the networks are more interpretable, training ought to be easier and faster, and the network only activates in areas of the feature space where it was actually trained, and has therewith the possibility to indicate that it "just doesn't know".

Initialization of an RBF network can be difficult and require prior knowledge. Before use of this function, you might want to read pp 172-183 of the SNNS User Manual 4.2. The initialization is performed in the current implementation by a call to RBF_Weights_Kohonen(0,0,0,0,0) and a successive call to the given initFunc (usually RBF_Weights). If this initialization doesn't fit your needs, you should use the RSNNS low-level interface to implement your own one. Have a look then at the demos/examples. Also, we note that depending on whether linear or logistic output is chosen, the initialization parameters have to be different (normally c(0,1,...) for linear and c(-4,4,...) for logistic output).

Value

an rsnns object.

References

Poggio, T. & Girosi, F. (1989), 'A Theory of Networks for Approximation and Learning'(A.I. Memo No.1140, C.B.I.P. Paper No. 31), Technical report, MIT ARTIFICIAL INTELLIGENCE LABORATORY.

Vogt, M. (1992), 'Implementierung und Anwendung von Generalized Radial Basis Functions in einem Simulator neuronaler Netze', Master's thesis, IPVR, University of Stuttgart. (in German)

Zell, A. et al. (1998), 'SNNS Stuttgart Neural Network Simulator User Manual, Version 4.2', IPVR, University of Stuttgart and WSI, University of Tübingen. https://www.ra.cs.uni-tuebingen.de/SNNS/welcome.html

Zell, A. (1994), Simulation Neuronaler Netze, Addison-Wesley. (in German)

Examples

## Not run: demo(rbf_irisSnnsR)
## Not run: demo(rbf_sin)
## Not run: demo(rbf_sinSnnsR)


inputs <- as.matrix(seq(0,10,0.1))
outputs <- as.matrix(sin(inputs) + runif(inputs*0.2))
outputs <- normalizeData(outputs, "0_1")

model <- rbf(inputs, outputs, size=40, maxit=1000, 
                     initFuncParams=c(0, 1, 0, 0.01, 0.01), 
                     learnFuncParams=c(1e-8, 0, 1e-8, 0.1, 0.8), linOut=TRUE)

par(mfrow=c(2,1))
plotIterativeError(model)
plot(inputs, outputs)
lines(inputs, fitted(model), col="green")

RSNNS documentation built on May 29, 2024, 4:37 a.m.