I'd like to solve the following optimization problem.
Y is a CxN matrix A is a CxC and diagonal matrix Q is a CxC and orthonormal matrix X is a CxN matrix
$$ min_{A,Q} {|| Y − AQX ||}^2_F $$
The question is how to optimize over A and Q.
Does anyone know how to take derivative wrt. diagonal and orthonormal matrix?