Skip to main content
SpringerLink
Log in

Signal Subspace Separation Based on the Divergence Measure of a Set of Wavelets Coefficients

  • Conference paper
Independent Component Analysis and Signal Separation (ICA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5441))

Abstract

The various scales of a signal maintain relations of dependence the ones with the others. Those can vary in time and reveal speed changes in the studied phenomenon. In the goal to establish these changes, one shall compute first the wavelet transform of a signal, on various scales. Then one shall study the statistical dependences between these transforms thanks to an estimator of mutual information (MI) called divergence. The time-scale representation of the sources representation shall be compared with the representation of the mixtures according to delay in time and in frequency.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoulas, A.: Encyclopedia for the Life Sciences, contribution 6.43.13.4 Frequency domain representation and singular value decomposition. UNESCO (2002)

    Google Scholar 

  2. Armstrong, J.S., Andress, J.G.: Exploratory analysis of marketing data: Trees vs. regression. Journal of Marketing Research 7, 487–492 (1970)

    Article  Google Scholar 

  3. Basseville, M.: Distance measure for signal processing and pattern recognition. Signal Process 18(4), 349–369 (1989)

    Article  MathSciNet  Google Scholar 

  4. Chan, K.P., Fu, A.W.: Efficient time series matching by wavelets. In: Proceedings of the 15th International Conference on Data Engineering, pp. 126–133 (1999)

    Google Scholar 

  5. Daubechies, I.: Ten lectures on wavelets, society for industrial and applied mathematics (1992)

    Google Scholar 

  6. Daubechies, I., Mallat, S., Willsky, A.S.: Introduction to the spatial issue on wavelet transforms and multiresolution signal analysis. IEEE Trans. Inform. Theory, 529–532 (1992)

    Google Scholar 

  7. Lemire, D.: A better alternative to piecewise linear time series segmentation. In: SIAM Data Mining 2007 (2007)

    Google Scholar 

  8. Lin, J., Vlachos, M., Keogh, E., Gunopulos, D.: Iterative incremental clustering of time series (2004)

    Google Scholar 

  9. Liu, J., Moulin, P.: Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients. IEEE Transactions on Image Processing 10(11), 1647–1658 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lütkepohl, H.: Handbook of Matrices, 1st edn. Wiley, Chichester (1997)

    MATH  Google Scholar 

  11. Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. and Mach. Intelligence 11(7), 674–693 (1989)

    Article  MATH  Google Scholar 

  12. Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.-M.: Clustering signals using wavelets. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 514–521. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Popivanov, I., Miller, R.J.: Similarity search over time-series data using wavelets. In: ICDE, pp. 212–221 (2002)

    Google Scholar 

  14. Rényi, A.: On measures on entropy and information. 4th Berkeley Symp. Math. Stat. and Prob. 1, 547–561 (1961)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBISC CNRS FRE 3190, Université d’Evry, France

    Vincent Vigneron

  2. CES CNRS-UMR 8174 Equipe SAMOS-MATISSE, Paris, France

    Aurélien Hazan

Authors
  1. Vincent Vigneron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aurélien Hazan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Electrical Engineering, ITE 324, University of Maryland, Baltimore County, 1000 Hilltop Circle, MD 21250, Baltimore, USA

    Tülay Adali

  2. Domaine Universitaire, GIPSA-lab, BP 46, 38402, Saint Martin d’Hères Cedex, France

    Christian Jutten

  3. Departamento de Microonda e Óptica (DMO), FEEC / Unicamp, Avenida Albert Einstein 400, 13083-852, Campinas, Sao Paulo, Brazil

    João Marcos Travassos Romano

  4. Centro Tecnológico, Curso de Engenharia Elétrica, Universidade Federal do Maranhão, Avenida dos Portugueses, s/n, Bacanga, 65080-040, São Luís, MA, Brazil

    Allan Kardec Barros

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vigneron, V., Hazan, A. (2009). Signal Subspace Separation Based on the Divergence Measure of a Set of Wavelets Coefficients. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00599-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00598-5

  • Online ISBN: 978-3-642-00599-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation