Equivariant nonstationary source separation

Most of source separation methods focus on stationary sources, so higher-order statistics is necessary for successful separation, unless sources are temporally correlated. For nonstationary sources, however, it was shown [Neural Networks 8 (1995) 4111 that source separation could be achieved by second-order decorrelation. In this paper, we consider the cost function proposed by Matsuoka et al. [Neural Networks 8 (1995) 4111 and derive natural gradient learning algorithms for both fully connected recurrent network and feedforward network. Since our algorithms employ the natural gradient method, they possess the equivariant property and find a steepest descent direction unlike the algorithm [Neural Networks 8 (1995) 411]. We also show that our algorithms are always locally stable, regardless of probability distributions of nonstationary sources. (C) 2002 Elsevier Science Ltd. All rights reserved.