Relative gradient on SO(N): case of source separation

Whitening is a popular method to reduce the complexity of the problems in ICA. In the linear instantaneous mixing model, the search space of the separation matrix is restricted to the special orthogonal group SO(N) by the prewhitening of the observations. This paper proposes a new learning rule in blind source separation using RGOSOG (relative gradient on SO(N)) method. We show that when the contrast function is the Renyi´s mutual information (RMI), the algorithm based on RGOSOG is easier to implement and the complexity of RGOSOG method is less than that of the conventional gradient descent method. Simulation illustrate that the new algorithm has the same performance on signal-to-distortion ratio as the conventional one.