Flag manifolds for subspace ICA problems

We investigate the use of the Riemannian optimization method over the flag manifold in subspace ICA problems such as independent subspace analysis (ISA) and complex ICA. In the ISA experiment, we use the Riemannian approach over the flag manifold together with an MCMC method to overcome the problem of local minima of the ISA cost function. Experiments demonstrate the effectiveness of both Riemannian methods – simple geodesic gradient descent and hybrid geodesic gradient descent, compared with the ordinary gradient method. Index Terms — Independent subspace analysis, complex ICA, natural gradient, geodesic, flag manifolds, Riemannian optimization metho