Conjugate gradient approach to blind separation of temporally correlated signals

The paper investigates the information geometry of the blind separation of temporally correlated signals. First, we introduce the Lie group and Riemannian metric to the manifold of nonsingular matrices. The explicit expression of the geodesic on the manifold is obtained. Furthermore, we introduce the concept of parallel translation of tangent vectors along the geodesic, which is necessary for implementing the conjugate gradient method. The conjugate gradient algorithm is then developed for training the parameter on the nonsingular matrix manifold. The proposed algorithm is applied to blind separation of temporally correlated signals. Computer simulations are also provided to demonstrate the learning performance of the conjugate gradient method on the Riemannian manifold.