Here is an optimization problem I came across in the paper titled "Learning the dependency structure of latent factors":
And here is the closed-form solution of it for S:
X is a PxN data matrix where P is the number of variables and N is the number of samples,
B is a PxK basis matrix which projects data X to a K-dimensional basis,
S is a KxN latent factor matrix of K factors,
Phi is a KxK symmetric matrix containing the structure among factors,
and sigma and rho are the scalars.
I didn't understand how the authors get to this derivation, and will be happy if someone can explain it. Thanks.