Abstract
We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew in source densities and subspaces using a generalization of the Normal Variance-Mean mixture model. We give closed form expressions for subspace likelihoods and parameter updates in the EM algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amari, S.-I., Cichocki, A.: Adaptive blind signal processing—neural network approaches. Proceedings of the IEEE 86(10), 2026–2047 (1998)
Andrews, D.F., Mallows, C.L.: Scale mixtures of normal distributions. J. Roy. Statist. Soc. Ser. B 36, 99–102 (1974)
Barndorff-Nielsen, O., Kent, J., Sørensen, M.: Normal variance-mean mixtures and z distributions. International Statistical Review 50, 145–159 (1982)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society Series B 39, 1–38 (1977)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Iteratively reweighted least squares for linear regression when errors are Normal/Independent distributed. In: Krishnaiah, P.R. (ed.) Multivariate Analysis V, pp. 35–57. North Holland Publishing Company, Amsterdam (1980)
Eltoft, T., Kim, T., Lee, T.-W.: Multivariate scale mixture of Gaussians modeling. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 799–806. Springer, Heidelberg (2006)
Gneiting, T.: Normal scale mixtures and dual probability densities. J. Statist. Comput. Simul. 59, 375–384 (1997)
Hyvärinen, A., Hoyer, P.O.: Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces. Neural Computation 12, 1705–1720 (2000)
Hyvärinen, A., Hoyer, P.O., Inki, M.: Topographic independent component analysis. Neural Computation 13(7), 1527–1558 (2001)
Kim, T., Attias, H., Lee, S.-Y., Lee, T.-W.: Blind source separation exploiting higher-order frequency dependencies. IEEE Transactions on Speech and Audio Processing, 15(1) (2007)
Kim, T., Eltoft, T., Lee, T.-W.: Independent vector analysis: An extension of ICA to multivariate components. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 165–172. Springer, Heidelberg (2006)
Palmer, J.A., Kreutz-Delgado, K., Makeig, S.: Super-Gaussian mixture source model for ICA. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 854–861. Springer, Heidelberg (2006)
Palmer, J.A., Kreutz-Delgado, K., Wipf, D.P., Rao, B.D.: Variational EM algorithms for non-gaussian latent variable models. In: Advances in Neural Information Processing Systems, NIPS 2005, MIT Press, Cambridge (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Palmer, J.A., Kreutz-Delgado, K., Rao, B.D., Makeig, S. (2007). Modeling and Estimation of Dependent Subspaces with Non-radially Symmetric and Skewed Densities. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-74494-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74493-1
Online ISBN: 978-3-540-74494-8
eBook Packages: Computer ScienceComputer Science (R0)