Abstract
The minimum support ICA algorithms currently use the extreme statistics difference (also called the statistical range) for support width estimation. In this paper, we extend this method by analyzing the use of (possibly averaged) differences between the N – m + 1-th and m-th order statistics, where N is the sample size and m is a positive integer lower than N/2. Numerical results illustrate the expectation and variance of the estimators for various densities and sample sizes; theoretical results are provided for uniform densities. The estimators are analyzed from the specific viewpoint of ICA, i.e. considering that the support widths and the pdf shapes vary with demixing matrix updates.
The authors are grateful to D. Erdogmus for having inspirited this work by fruitful discussion on expectation and variance of cdf differences and m-spacings.
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.
References
Vrins, F., Jutten, C., Verleysen, M.: SWM: a Class of Convex Contrasts for Source Separation. In: Proc. ICASSP, IEEE Int. Conf. on Acoustics, Speech and Sig. Process., Philadelphia, USA, pp. V.161–V.164 (2005)
Vrins, F., Verleysen, M.: Minimum Support ICA Using Order Statistics. Part II: Performance Analysis. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 270–277. Springer, Heidelberg (2006)
Cruces, S., Duran, I.: The Minimum Support Criterion for Blind Source Extraction: a Limiting Case of the Strengthened Young’s Inequality. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 57–64. Springer, Heidelberg (2004)
Pham, D.-T.: Blind Separation of Instantaneous Mixture of Sources Based on Order Statistics. IEEE Trans. Sig. Process. 48(2), 363–375 (2000)
Ebrahimi, N., Soofi, E.S., Zahedi, H.: InformationProperties ofOrder Statistics and Spacings. IEEE Trans. Info. Theory 50(1), 177–183 (2004)
Spiegel, M.R.: Mathematical Handbook of Formulas and Tables. McGraw-Hill, New York (1974)
Papadatos, N.: Upper Bound for the Covariance of Extreme Order Statistics From a Sample of Size Three. Indian J. of Stat., Series A, Part 2 61, 229–240 (1999)
David, H.A.: Order Statistics. Wiley series in probability and mathematical statistics. Wiley, New York (1970)
Even, J.: Contributions à la Séparation de Sources à l’Aide de Staitistiques d’Ordre. PhD Thesis, Univ. J. Fourier, Grenoble, France (2003)
Blanco, Y., Zazo, S.: An Overview of BSS Techniques Based on Order Statistics: Formulation and Implementation Issues. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 73–80. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vrins, F., Verleysen, M. (2006). Minimum Support ICA Using Order Statistics. Part I: Quasi-range Based Support Estimation. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_33
Download citation
DOI: https://doi.org/10.1007/11679363_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32630-4
Online ISBN: 978-3-540-32631-1
eBook Packages: Computer ScienceComputer Science (R0)