Abstract
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.
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References
Jutten, C., Hérault, J.: Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing 24, 1–10 (1991)
Comon, P.: Independent component analysis. a new concept? Signal Processing 36, 62–83 (1994)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent component analysis. Wiley, New York (2001)
Bach, F.R., Jordan, M.I.: Tree-dependent component analysis. In: Proc. the 18th Conference on Uncertainty in Artificial Intelligence, UAI-2002 (2002)
Hyvärinen, A.: A unifying model for blind separation of independent sources. Signal Processing 85, 1419–1427 (2005)
Hyvärinen, A., Hoyer, P.O., Inki, M.: Topographic independent component analysis. Neural Computation 13, 1525–1558 (2001)
Hyvärinen, A., Hurri, J.: Blind separation of sources that have spatiotemporal dependencies. Signal Processing 84, 247–254 (2004)
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)
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)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. on Neural Networks 10, 626–634 (1999)
Ferguson, T.S.: A method of generating best asymptotically normal estimates with application to estimation of bacterial densities. Annals of Mathematical Statistics 29, 1046–1062 (1958)
Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM Journal on Matrix Analysis and Applications 20, 303–353 (1998)
Hyvärinen, A.: The fixed-point algorithm and maximum likelihood estimation for independent component analysis. Neural Processing Letters 10, 1–5 (1999)
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Hyvärinen, A., Shimizu, S. (2006). A Quasi-stochastic Gradient Algorithm for Variance-Dependent Component Analysis. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840930_22
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DOI: https://doi.org/10.1007/11840930_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38871-5
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