gtm_stp1 {gtm}R Documentation

Generates the components of a GTM with a 1D latent space

Description

1-5 lines

Usage

gtm_stp1(T, noLatVarSmpl, noBasFn, s)

Arguments

T target data, to be modelled by the GTM.
noLatVarSmpl number of samples in the latent variable space
noBasFn number of basis functions
s the width of basis functions relative to the distance between two neighbouring basis function centres, i.e. if s = 1, the basis functions will have widths (std.dev) equal to (i.e. 1 times) the distance between two neighbouring basis function centres.

Value

List with the following components

X the grid of data points making up the latent variable sample; a vector of length noLatVarSmpl, in which each row is a data point
MU a noBasFn-element vector holding the coordinates of the centres of the basis functions
FI the activations of the basis functions when fed the latent variable sample X, and a bias unit fixed to 1.0; a matrix with the same number of rows as X and noBasFn+1 columns (+1 for the bias)
W the initial matrix of weights, mapping the latent variable sample X linearly onto the first principal component of the target data (T)
beta - the intial value for the inverse variance of the data space noise model

Note

The latent variable sample is constructed as a uniform grid on the interval [-1, 1]. Similarly the centres of the basis function are gridded uniformly over the latent variable sample, with equal standard deviation, set relative to the distance between two centres. The initial linear mapping maps mean and std.devs. 1:1 from the latent to the target sample along the principal component.

See Also

gtm_stp2

Examples

  T = matrix(3:61/20, ncol=1);
  T = cbind(T, T + 1.25 * sin(2*T));
  # plot of sample data 
  plot(T[,1], T[,2], col='red', pch=21, xlim=c(0, 3.5), ylim=c(0,3.5))
    
  # setup and training
  stpResult = gtm_stp1(T, 20, 5, 2);
  stpY = stpResult$FI 
  
  # plot initialized data points
  matplot(stpY[,1], stpY[,2], col='green', add=TRUE, type='l')
  matplot(stpY[,1], stpY[,2], col='green', add=TRUE, type='p', pch=23)

[Package gtm version 1.0 Index]