Robust Independent Component Analysis Based on Two Scatter Matrices
Oja, Sirkiä, and Eriksson (2006) and Ollila, Oja, and Koivunen (2007) showed that, under general assumptions, any two scatter matrices with the so called independent components property can be used to estimate the unmixing matrix for the independent component analysis (ICA). The method is a generalization of Cardoso’s (Cardoso, 1989) FOBI estimate which uses the regular covariance matrix and a scatter matrix based on fourth moments. Different choices of the two scatter matrices are compared in a simulation study. Based on the study, we recommend always the use of two robust scatter matrices. For possible asymmetric independent components, symmetrized versions of the scatter matrix estimates should be used.
Amari, S., Cichocki, A., and Yang, H. (1996). A new learning algorithm for blind source separation. In Advances in neural information processing systems 8 (p. 757-763).
Cambridge, MA.: MIT Press.
Cardoso, J. (1989). Source separation using higher order moments. In Proceedings of IEEE international conference on acustics, speech and signal processing (p. 2109-
Dümbgen, L. (1998). On Tyler’s M-functional of scatter in high dimension. Annals of Institute of Statistical Mathematics, 50, 471-491.
Hettmansperger, T. P., and Randles, R. H. (2002). A practical affine equivariant multivariate median. Biometrika, 89, 851–860.
Hyvärinen, A., Karhunen, J., and Oja, E. (2001). Independent component analysis. New
Hyvärinen, A., and Oja, E. (1997). A fast fixed-point algorithm for independent component analysis. Neural Computation, 9, 1483-1492.
Hyvärinen, A., and Oja, E. (2000). Independent component analysis: Algorithms and applications. Neural Networks, 13, 411-430.
Marchini, J., Heaton, C., and Ripley, B. (2006). fastICA: FastICA algorithms to perform ICA and projection pursuit [Computer software manual]. (R package version 1.1-8)
Maronna, R., Martin, R., and Yohai, V. (2006). Robust statistics. Chichester: Wiley.
Nordhausen, K., Oja, H., and Tyler, D. (2006). ICS: ICS / ICA computation based on two scatter matrices [Computer software manual]. (R package version 0.1-2)
Oja, H., Sirkiä, S., and Eriksson, J. (2006). Scatter matrices and independent component analysis. Austrian Journal of Statistics, 35, 175-189.
Ollila, E., Oja, H., and Koivunen, V. (2007). Complex-valued ICA based on a pair of generalized covariance matrices. (Conditionally accepted by Computational Statistics & Data Analysis)
R Development Core Team. (2006). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Available from
http://www.R-project.org (ISBN 3-900051-07-0)
Sirkiä, S., Taskinen, S., and Oja, H. (2007). Symmetrized M-estimators of multivariate scatter. Journal of Multivariate Analysis, 98, 1611-1629.
Tyler, D. E. (1987). A distribution-free M-estimator of multivariate scatter. Annals of Statistics, 15, 234-251.
How to Cite
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.