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 to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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).
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.
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.
I. S. Dhillon and S. Sra, “Generalized Nonnegative Matrix Approximations with Bregman Divergences,” in Proc. NIPS, Vancouver, BC, 2005.
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.
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.
P. O. Hoyer, “Non-negative Matrix Factorization with Sparseness Constraints,” J. Mach. Learn. Res., vol. 5, 2004, pp. 1457–1469.
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.
D. D. Lee and H. S. Seung, “Learning the Parts of Objects by Non-negative Matrix Factorization,” Nature, vol. 401, 1999, pp. 788–791.
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.
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.
C.-J. Lin, “Projected Gradient Methods for Non-negative Matrix Factorization,” Technical report, Department of Computer Science, National Taiwan University, 2005.
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.
J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2000.
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.
P. Sajda, D. Shuyan, and L. Parra, “Recovery of Constituent Spectra Using Non-negative Matrix Factorization,” Proc. SPIE, vol. 5207, 2003, pp. 321–331.
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.
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.
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.
W. Wang and T. Adalı, “Constrained ICA and its Application to Raman Spectroscopy,” in AP-S/URSI Symposium 2005, Washington, DC.
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.
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.
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
- Raman spectroscopy
- non-negative matrix factorization