Abstract
Renyi’s entropy-based criterion has been proposed as an objective function for independent component analysis because of its relationship with Shannon’s entropy and its computational advantages in specific cases. These criteria were suggested based on “convincing” experiments. However, there is no theoretical proof that globally maximizing those functions would lead to separate the sources; actually, this was implicitly conjectured. In this paper, the problem is tackled in a theoretical way; it is shown that globally maximizing the Renyi’s entropy-based criterion, in its general form, does not necessarily provide the expected independent signals. The contrast function property of the corresponding criteria simultaneously depend on the value of the Renyi parameter, and on the (unknown) source densities.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Comon, P.: Independent component analysis, a new concept? Signal Processing 36(3), 287–314 (1994)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Series in Telecommunications. Wiley and Sons, Inc, Chichester (1991)
Dembo, A., Cover, T.M., Thomas, J.A.: Information theoretic inequalities. IEEE Transactions on Information Theory 37(6), 1501–1518 (1991)
Erdogmus, D., Hild, K.E., Principe, J.: Blind source separation using renyi’s mutual information. IEEE Signal Processing Letters 8(6), 174–176 (2001)
Erdogmus, D., Hild, K.E., Principe, J.: Blind source separation using renyi’s α-marginal entropies. Neurocomputing 49(49), 25–38 (2002)
Gray, R., Davisson, L.: An Introduction to Statistical Signal Processing. Cambridge University Press, Cambridge (2004)
Hild, K.E., Erdogmus, D., Principe, J.: An analysis of entropy estimators for blind source separation. Signal Processing, 86, 174–176, 182–194 (2006)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent component analysis. John Willey and Sons, Inc. New York (2001)
Pham, D.-T.: Entropy of a variable slightly contaminated with another. IEEE Signal Processing Letters 12(7), 536–539 (2005)
Renyi, A.: On measures of entropy and information. Selected papers of Alfred Renyi 2, 565–580 (1976)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vrins, F., Pham, DT., Verleysen, M. (2007). Is the General Form of Renyi’s Entropy a Contrast for Source Separation?. 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_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-74494-8_17
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)