A Quasi-stochastic Gradient Algorithm for Variance-Dependent Component Analysis
We discuss the blind source separation problem where the sources are not independent but are dependent only through their variances. Some estimation methods have been proposed on this line. However, most of them require some additional assumptions: a parametric model for their dependencies or a temporal structure of the sources, for example. In previous work, we have proposed a generalized least squares approach using fourth-order moments to the blind source separation problem in the general case where those additional assumptions do not hold. In this article, we develop a simple optimization algorithm for the least squares approach, or a quasi-stochastic gradient algorithm. The new algorithm is able to estimate variance-dependent components even when the number of variables is large and the number of moments is computationally prohibitive.
KeywordsIndependent Component Analysis Independent Component Analysis Blind Source Separation Generalize Little Square Independent Component Analysis Algorithm
Unable to display preview. Download preview PDF.
- 4.Bach, F.R., Jordan, M.I.: Tree-dependent component analysis. In: Proc. the 18th Conference on Uncertainty in Artificial Intelligence, UAI-2002 (2002)Google Scholar
- 6.Hyvärinen, A., Hoyer, P.O., Inki, M.: Topographic independent component analysis. Neural Computation 13, 1525–1558 (2001)Google Scholar
- 8.Kawanabe, M., Müller, K.R.: Estimating functions for blind separation when sources have variance-dependencies. In: Proc. 5th International Conference on ICA and Blind Source Separation, Granada, Spain, pp. 136–143 (2004)Google Scholar
- 9.Shimizu, S., Hyvärinen, A., Kano, Y.: A generalized least squares approach to blind separation of sources which have variance dependency. In: Proc. IEEE Workshop on Statistical Signal Processing, SSP 2005 (2005)Google Scholar