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


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.

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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

An erratum to this article is available at

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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).

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  • Raman spectroscopy
  • non-negative matrix factorization