Generates the components of a GTM with a 1D latent space.
[X, MU, FI, W, beta] = gtm_stp1(T, noLatVarSmpl, noBasFn, s)
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.
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
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.