Skip to main content

Matrix Estimation Based on Normal Vector of Hyperplane in Sparse Component Analysis

  • Conference paper
Advances in Swarm Intelligence (ICSI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6146))

Included in the following conference series:

Abstract

This paper discusses the matrix estimation for sparse component analysis under the k-SCA condition. Here, to estimate the mixing matrix using hyperplane clustering, we propose a new algorithm based on normal vector for hyperplane. Compared with the Hough SCA algorithm, we give a method to calculate normal vector for hyperplane, and the algorithm has lower complexity and higher precision. Two examples demonstrates its performance.

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

Access this chapter

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. Cardoso, J.F.: Blind signals separation: Statistical principles. Proc. IEEE 86, 1129–1159 (1998)

    Article  Google Scholar 

  2. Zhang, J., Xie, S., Wang, J.: Multi-input single-output neural network blind separation algorithm based on penalty function. DCDIS-Series B-Applications & Algorithms Suppl. SI, 353–361 (2003)

    Google Scholar 

  3. Xie, S., He, Z., Gao, Y.: Adaptive Theory of Signal Processing. Chinese Science Press, Beijing (2006)

    Google Scholar 

  4. Xie, S., He, Z., Fu, Y.: A note on Stone’s conjecture of blind signal separation. Neural Computation 17, 321–330 (2005)

    Article  Google Scholar 

  5. Cichocki, A., Amari, S.: Adaptive blind signal and image processing: learning algorithms and applications. Wiley, New York (2002)

    Book  Google Scholar 

  6. Bofill, P., Zibulevsky, M.: Underdetermined blind source separation using sparse representations. Signal Processing 81, 2353–2362 (2001)

    Article  MATH  Google Scholar 

  7. Li, Y., Amari, S., Cichocki, A., et al.: Underdetermined Blind Source Separation Based on Sparse Representation. IEEE Transactions on Signal Processing 54(2), 423–437 (2006)

    Article  Google Scholar 

  8. He, Z., Xie, S., Fu, Y.: FIR convolutive BSS based on sparse representation. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3497, pp. 532–537. Springer, Heidelberg (2005)

    Google Scholar 

  9. He, Z., Cichocki, A.: K-EVD Clustering and its Applications to Sparse Component Analysis. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 90–97. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Georgiev, P.G., Theis, F.J., Cichocki, A.: Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Transactions of NeuralNetworks 16(4), 992–996 (2005)

    Article  Google Scholar 

  11. Theis, F.J., Georgiev, P.G., Cichocki, A.: Robust overcomplete matrix recovery for sparse sources using a generalized hough transform. In: Proceedings of 12th European Symposium on Artificial Neural Networks (ESANN 2004), Bruges, Belgium, April 2004, pp. 343–348 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gao, F., Sun, G., Xiao, M., Lv, J. (2010). Matrix Estimation Based on Normal Vector of Hyperplane in Sparse Component Analysis. In: Tan, Y., Shi, Y., Tan, K.C. (eds) Advances in Swarm Intelligence. ICSI 2010. Lecture Notes in Computer Science, vol 6146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13498-2_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13498-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13497-5

  • Online ISBN: 978-3-642-13498-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics