A Robust Objective Function of Joint Approximate Diagonalization
Joint approximate diagonalization (JAD) is a method solving blind source separation, which can extract non-Gaussian sources without any other prior knowledge. However, it is not robust when the sample size is small because JAD is based on an algebraic objective function. In this paper, a new robust objective function of JAD is derived by an information theoretic approach. It has been shown in previous works that the “true” probabilistic distribution of non-diagonal elements of approximately-diagonalized cumulant matrices in JAD is Gaussian with a fixed variance. Here, the distribution of the diagonal elements is also approximated as Gaussian where the variance is an adjustable parameter. Then, a new objective function is defined as the likelihood of the distribution. Numerical experiments verify that the new objective function is effective when the sample size is small.
Keywordsblind source separation independent component analysis joint approximate diagonalization information theoretic approach
Unable to display preview. Download preview PDF.
- 1.Amari, S., Cichocki, A.: A new learning algorithm for blind signal separation. In: Touretzky, D., Mozer, M., Hasselmo, M. (eds.) Advances in Neural Information Processing Systems 8, pp. 757–763. MIT Press, Cambridge (1996)Google Scholar
- 3.Cardoso, J.F., Souloumiac, A.: Blind beamforming for non Gaussian signals. IEE Proceedings-F 140(6), 362–370 (1993)Google Scholar
- 4.Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Wiley (2002)Google Scholar
- 5.Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley (2001)Google Scholar