Latent space posterior probability distribution for a given data point.
This function calculates the posterior probability distribution induced in the latent space of a trained GTM model for a given data point, and returns it in a format suitable for MATLAB's 2D or 3D graphic plotting routines, depending on the latent space dimensionality.
[xl, yl, p] = gtm_ppd(t, Y, beta, X, xDim, yDim)
[xl, p] = gtm_ppd(t, Y, beta, X)
t - a point in the data space; 1-by-D
Y - centres of the Gaussian mixture generated by the GTM in the data space, Y = FI*W; K-by-D
beta - variance of Gaussian mixture; scalar
X - latent sample
xDim, yDim - number of points along the 2 dimensions of the latent space meshgrid sample
xl, yl - latent sample; if the latent space is 2D, xl and yl are mesh matrices; if it is 1D, xl
is identical to X
p - posterior distribution over latent space given data point t; if the latent space is 2D, p is
a mesh matrix, otherwise it is a vector of same length as xl
If the latent sample X is 2 dimensional, it is assumed to have been constructed from a mesh-grid, e.g. as if generated by gtm_stp2