Abstract
A framework named copula component analysis (CCA) for blind source separation is proposed as a generalization of independent component analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components may be dependent by certain structure which is represented by Copula. By incorporating dependency structure, much accurate estimation can be made in principle in the case that the assumption of independence is invalidated. A two phrase inference method is introduced for CCA which is based on the notion of multi-dimensional ICA. Simulation experiments preliminarily show that CCA can recover dependency structure within components while ICA does not.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Comon, P.: Independent component analysis - A new concept? Signal Processing 36, 287–314 (1994)
Bell, A., Sejnowski, T.: An information-maximization approach to blind separation and blind deconvolution. Neural Comp. 7, 1129–1159 (1995)
Amari, S., Cichocki, A., Yang, H.H.: A new learning algorithm for blind source separation. In: Advances in Neural Information Processing, pp. 757–763. MIT Press, Cambridge (1996)
Cardoso, J.-F., Laheld, B.H.: Equivariant adaptive source separation. IEEE Transactions on Signal Processing 44, 3017–3030 (1996)
Pham, D.T., Garat, P.: Blind separation of mixture of independent sources through a quasi-maximum likelihood approach. IEEE Transactions on Signal Processing 45, 1712–1725 (1997)
Cardoso, J.-F.: Multidimensional independent component analysis, Acoustics, Speech, and Signal Processing. In: ICASSP 1998. Proceedings of the 1998 IEEE International Conference on, vol. 4, pp. 1941–1944 (1998)
Bach, F.R., Jordan, M.I.: Beyond independent components: Trees and clusters. Journal of Machine Learning Research 4, 1205–1233 (2003)
Hyvärinen, A., Hoyer, P.O., Inki, M.: Topographic Independent Component Analysis. Neural Computation 13, 1527–1558 (2001)
Nelsen, R.B.: An Introduction to Copulas. Lecture Notes in Statistics. Springer, New York (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, J., Sun, Z. (2007). Copula Component Analysis. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-74494-8_10
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)