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

  • Hualiang Li
  • Tülay Adal
  • Wei Wang
  • Darren Emge
  • Andrzej Cichocki
  • Andrzej Cichocki


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.


Raman spectroscopy non-negative matrix factorization NMFOC 


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  1. 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).Google Scholar
  2. 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.Google Scholar
  3. 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.Google Scholar
  4. 4.
    I. S. Dhillon and S. Sra, “Generalized Nonnegative Matrix Approximations with Bregman Divergences,” in Proc. NIPS, Vancouver, BC, 2005.Google Scholar
  5. 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.Google Scholar
  6. 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.CrossRefGoogle Scholar
  7. 7.
    P. O. Hoyer, “Non-negative Matrix Factorization with Sparseness Constraints,” J. Mach. Learn. Res., vol. 5, 2004, pp. 1457–1469.Google Scholar
  8. 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.Google Scholar
  9. 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.CrossRefGoogle Scholar
  10. 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.Google Scholar
  11. 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. 12.
    C.-J. Lin, “Projected Gradient Methods for Non-negative Matrix Factorization,” Technical report, Department of Computer Science, National Taiwan University, 2005.Google Scholar
  13. 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.Google Scholar
  14. 14.
    J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2000.Google Scholar
  15. 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.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.Google Scholar
  18. 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.Google Scholar
  19. 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.Google Scholar
  20. 20.
    W. Wang and T. Adalı, “Constrained ICA and its Application to Raman Spectroscopy,” in AP-S/URSI Symposium 2005, Washington, DC.Google Scholar
  21. 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.Google Scholar
  22. 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.Google Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hualiang Li
    • 1
  • Tülay Adal
    • 1
  • Wei Wang
    • 1
  • Darren Emge
    • 2
  • Andrzej Cichocki
    • 3
  • Andrzej Cichocki
    • 4
  1. 1.Department of CSEEUniversity of Maryland Baltimore CountyBaltimoreUSA
  2. 2.US Army ResearchAberdeen Proving GroundsAberdeenUSA
  3. 3.Laboratory for Advanced Brain Signal ProcessingBrain Science InstituteSaitamaJapan
  4. 4.Warsaw University of TechnologyWarsawPoland

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