brnn (version 0.9.3)

initnw: Initialize networks weights and biases

Description

Function to initialize the weights and biases in a neural network. It uses the Nguyen-Widrow (1990) algorithm.

Usage

initnw(neurons,p,n,npar)

Value

A list containing initial values for weights and biases. The first \(s\) components of the list contains vectors with the initial values for the weights and biases of the \(k\)-th neuron, i.e. \((\omega_k, b_k, \beta_1^{(k)},...,\beta_p^{(k)})'\).

Arguments

neurons

Number of neurons.

p

Number of predictors.

n

Number of cases.

npar

Number of parameters to be estimate including only weights and biases, and should be equal to \(neurons \times (1+1+p)+1\).

Details

The algorithm is described in Nguyen-Widrow (1990) and in other books, see for example Sivanandam and Sumathi (2005). The algorithm is briefly described below.

• 1.-Compute the scaling factor \(\theta=0.7 p^{1/n}\).

• 2.- Initialize the weight and biases for each neuron at random, for example generating random numbers from \(U(-0.5,0.5)\).

• 3.- For each neuron:

  • compute \(\eta_k=\sqrt{\sum_{j=1}^p (\beta_j^{(k)})^2}\),

  • update \((\beta_1^{(k)},...,\beta_p^{(k)})'\), $$\beta_j^{(k)}=\frac{\theta \beta_j^{(k)}}{\eta_k}, j=1,...,p,$$

  • Update the bias \((b_k)\) generating a random number from \(U(-\theta,\theta)\).

References

Nguyen, D. and Widrow, B. 1990. "Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights", Proceedings of the IJCNN, 3, 21-26.

Sivanandam, S.N. and Sumathi, S. 2005. Introduction to Neural Networks Using MATLAB 6.0. Ed. McGraw Hill, First edition.

Examples

if (FALSE) {
#Load the library
library(brnn)

#Set parameters
neurons=3
p=4
n=10
npar=neurons*(1+1+p)+1
initnw(neurons=neurons,p=p,n=n,npar=npar)

}