Riemannian Newton's method for joint diagonalization on the Stiefel manifold with application to ICA
Hiroyuki Sato · arXiv (Cornell University) · 2014
Joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. It is known that this problem can be formulated as an optimization problem on the Stiefel manifold. Riemannian optimization techniques can be used to solve this optimization problem. Among the available techniques, this article provides Riemannian Newton's method for the joint diagonalization problem, which has the quadratic convergence property. In particular, it is shown that the resultant Newton's equation can be effectively solved by means of the Kronecker product and vec operator, which reduces the dimension of the equation. Numerical experiments are performed to show that the proposed method improves the accuracy of an approximate solution of the problem.