Skip to main content
SpringerLink
Log in

Non-negative Matrix Factorization with Orthogonality Constraints and its Application to Raman Spectroscopy

  • Published:
The Journal of VLSI Signal Processing Systems for Signal, Image, and Video Technology Aims and scope Submit manuscript

An Erratum to this article was published on 21 August 2007

Abstract

We introduce non-negative matrix factorization with orthogonality constraints (NMFOC) for detection of a target spectrum in a given set of Raman spectra data. An orthogonality measure is defined and two different orthogonality constraints are imposed on the standard NMF to incorporate prior information into the estimation and hence to facilitate the subsequent detection procedure. Both multiplicative and gradient type update rules have been developed. Experimental results are presented to compare NMFOC with the basic NMF in detection, and to demonstrate its effectiveness in the chemical agent detection problem.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Berry, M. Browne, A. Langville, P. Pauca, and R. Plemmons, “Algorithms and Applications for Approximate Nonnegative Matrix Factorization, ” Comput. Stat. Data Anal., 2006 (in press).

  2. A. Cichocki, R. Zdunek, and S. Amari, “Csiszár’s Divergence for Non-negative Matrix Factorization: Family of New Algorithms,” in Proc. 6th Int. Conf. ICA and BSS, Charleston SC, March 5–8, 2006, Springer LNCS, vol. 3889, pp. 32–39.

  3. D. Donoho and V. Stodden, “When Does Non-negative Matrix Factorization Give a Correct Decomposition into Parts?” in Proc. Neural Information Processing Systems, vol. 16, 2003, pp. 1141–1149.

  4. I. S. Dhillon and S. Sra, “Generalized Nonnegative Matrix Approximations with Bregman Divergences,” in Proc. NIPS, Vancouver, BC, 2005.

  5. C. Gobinet, E. Perrin, and R. Huez, “Application of Nonnegative Matrix Factorization to Fluorescence Spectroscopy,” in Proc. EUSIPCO 2004, Vienna, Austria, Sept. 6–10, 2004.

  6. F. Guimet, R. Boqué, and J. Ferré, “Application of Non-negative Matrix Factorization Combined with Fisher’s Linear Discriminant Analysis for Classification of Olive Oil Excitation–emission Fluorescence Spectra,” Chemometr. Intell. Lab. Syst., vol. 81, 2006, pp. 94–106.

    Article  Google Scholar 

  7. P. O. Hoyer, “Non-negative Matrix Factorization with Sparseness Constraints,” J. Mach. Learn. Res., vol. 5, 2004, pp. 1457–1469.

    Google Scholar 

  8. ITT Industries, Advanced Engineering and Sciences Division, “Tests of Laser Interrogation of Surface Agents System for On-the-move Standoff Sensing of Chemical Agents,” in Proc. Int. Symp. Spect. Sensing Research, 2003.

  9. D. D. Lee and H. S. Seung, “Learning the Parts of Objects by Non-negative Matrix Factorization,” Nature, vol. 401, 1999, pp. 788–791.

    Article  Google Scholar 

  10. D. D. Lee and H. S. Seung, “Algorithms for Non-negative Matrix Factorization,” in Proc. Neural Information Processing Systems, vol. 13, 2000, pp. 556–562.

  11. S. Z. Li, X. Hou, H. Zhang, and Q. Cheng, “Learning Spatially Localized, Parts-based Representation,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., vol. 1, 2001, pp. 207–212.

    Google Scholar 

  12. C.-J. Lin, “Projected Gradient Methods for Non-negative Matrix Factorization,” Technical report, Department of Computer Science, National Taiwan University, 2005.

  13. S. Moussaoui, D. Brie, C. Carteret, and A. Mohammad-Djafari, “Application of Bayesian Non-negative Source Separation to Mixture Analysis in Spectroscopy,” in Proc. 24th Int. Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Max-Planck Institute, Garching, Munich, Germany, July 2004, pp. 25–30.

  14. J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2000.

  15. A. Pascual-Montano, J. M. Carazo, K. Kochi, D. Lehmann, and R. D. Pascual-Marqui, “Nonsmooth Nonnegative Matrix Factorization (nsNMF),” IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 3, 2006, pp. 403–415, Mar.

    Article  Google Scholar 

  16. P. Sajda, D. Shuyan, and L. Parra, “Recovery of Constituent Spectra Using Non-negative Matrix Factorization,” Proc. SPIE, vol. 5207, 2003, pp. 321–331.

    Article  Google Scholar 

  17. F. Sha, L. K. Saul, and D. D. Lee “Multiplicative Updates for Nonnegative Quadratic Programming in Support Vector Machines,” in Proc. Neural Information Processing Systems, vol. 15, MIT Press, 2003.

  18. R. Salakhutdinov, S. Roweis, and Z. Ghahramani, “On the Convergence of Bound Optimization Algorithms,” in Proc. Conf. on Uncertainty in Artificial Intelligence, vol. 19, 2003, pp. 509–516.

  19. S. Sigurdsson, J. Larsen, P. Philipsen, M. Gniadecka, H. Wulf, and L. Hansen, “Estimating and Suppressing Background in Raman Spectra with an Artificial Neural Network,” Informatics and Mathematical Modeling, Technical Univ. Denmark, Tech. Rep. 2003–2020, 2003.

  20. W. Wang and T. Adalı, “Constrained ICA and its Application to Raman Spectroscopy,” in AP-S/URSI Symposium 2005, Washington, DC.

  21. W. Wang, T. Adalı, H. Li, and D. Emge, “Detection Using Correlation Bound and its Application to Raman Spectroscopy,” in 2005 IEEE Workshop on Machine Learning for Signal Processing, September, 2005, pp. 259–264.

  22. R. Zdunek and A. Cichocki, “Non-negative Matrix Factorization with Quasi-Newton Optimization,” in Proc. 8th Int. Conf. on Artificial Intelligence and Soft Computing, ICAISC, Zakopane, Poland, 25–29 June, 2006, Springer Lectures Notes in Artificial Intelligence, vol. 4029, pp. 870–879.

Download references

Author information

Authors and Affiliations

  1. Department of CSEE, University of Maryland Baltimore County, Baltimore, MD, USA

    Hualiang Li, Tülay Adal & Wei Wang

  2. US Army Research, Aberdeen Proving Grounds, Aberdeen, MD, 21010, USA

    Darren Emge

  3. Laboratory for Advanced Brain Signal Processing, Brain Science Institute, Riken 2-1 Hirosawa, Wako-shi, Saitama, 351-0198, Japan

    Andrzej Cichocki

  4. Warsaw University of Technology, Warsaw, Poland

    Andrzej Cichocki

Authors
  1. Hualiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tülay Adal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Darren Emge
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrzej Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Andrzej Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hualiang Li.

Additional information

This project is supported by Edgewood Chemical Biological Center, US Army RDECOM under contract no: W91ZLK-04-P-0950.

An erratum to this article can be found at http://dx.doi.org/10.1007/s11265-007-0096-z

An erratum to this article is available at http://dx.doi.org/10.1007/s11265-007-0096-z.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H., Adal, T., Wang, W. et al. Non-negative Matrix Factorization with Orthogonality Constraints and its Application to Raman Spectroscopy. J VLSI Sign Process Syst Sign Im 48, 83–97 (2007). https://doi.org/10.1007/s11265-006-0039-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11265-006-0039-0

Keywords

Search

Navigation