The observations are generated using probabilistic ICA:
$$ X_i(v) = \sum_{j=1}^q A_{i,j} S_j(v) + \epsilon_i(v) , $$
where \(S_j, j=1,...,q\) are the latent components, \(A_{i,j}\) is
the mixing coeffecient and \(\epsilon_i\) is the noise term.
Specifically, the number of components in this function is \(q = 3\),
with each of them being a specific geometric shape. The mixing coefficient matrix
is generated with a von Mises-Fisher distribution with the concentration parameter
being zero, which means it is uniformly distributed on the sphere. \(\epsilon_i\)
is a i.i.d. Gaussian noise term with 0 mean and user-specified variance.