Returns a weight matrix initialised using principal components.
The returned weight matrix maps the mean of the latent variable to the mean of the target variable, and the L-dimensional latent variable variance to the variance of the target data along its L first principal components.
An initial value for beta can also be calculated, based on the noise of the data (the "L+1"th eigenvalue) and the interdistances between Gaussian mixture centres in the data space.
[W, beta] = gtm_pci(T, X, FI)
W = gtm_pci(T, X, FI)
T - target distribution sample; one data point per row; N-by-D
X - the latent distribution sample, K-by-L
FI - basis functions' activation when fed the latent data, X, plus a bias, K-by-(M+1)
W - the initialised weight matrix, (K+1)-by-D
beta - the initial beta value, scalar. This is an optional output argument; if ommitted, the corresponding
(rather time consuming) calculations are ommitted too.
The first dimension (column) of X will map to the first principal component, the second dimension (column) of X will map to the second principal component, and so on. This may be of importance for the choice of sampling density along the different dimensions of X, if it differs between different dimensions