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Constrained Regularization:  Hybrid Method for Multivariate Calibration

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G. R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 6-014, Cambridge, Massachusetts 02139
Cite this: Anal. Chem. 2007, 79, 1, 234–239
Publication Date (Web):November 18, 2006
https://doi.org/10.1021/ac060732v
Copyright © 2007 American Chemical Society

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    Abstract

    We present a hybrid multivariate calibration method, constrained regularization (CR), and demonstrate its utility via numerical simulations and experimental Raman spectra. In this new method, multivariate calibration is treated as an inverse problem in which an optimal balance between model complexity and noise rejection is achieved with the inclusion of prior information in the form of a spectral constraint. A key feature is that the constraint is incorporated in a flexible manner, allowing the minimization algorithm to arrive at the optimal solution. We demonstrate that CR, when used with an appropriate constraint, is superior to methods without prior information, such as partial least-squares, and is less susceptible to spurious correlations. In addition, we show that CR is more robust than methods in which the constraint is rigidly incorporated, such as hybrid linear analysis, when the exact spectrum of the analyte of interest as it appears in the sample is not available. This situation can occur as a result of experimental or sample variations and often arises in complex or turbid samples such as biological tissues.

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     To whom correspondence should be addressed. E-mail:  [email protected].

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    18. Andrew J. Berger. Raman Spectroscopy of Blood and Urine Specimens. 2010, 385-404. https://doi.org/10.1007/978-3-642-02649-2_16
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    21. Wei‐Chuan Shih, Kate L. Bechtel, Michael S. Feld, Mark A. Arnold, Gary W. Small. Introduction to Spectroscopy for Noninvasive Glucose Sensing. 2009, 331-356. https://doi.org/10.1002/9780470567319.ch12
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    23. John H. Kalivas, Gabriel G. Siano, Erik Andries, Hector C. Goicoechea. Calibration Maintenance and Transfer Using Tikhonov Regularization Approaches. Applied Spectroscopy 2009, 63 (7) , 800-809. https://doi.org/10.1366/000370209788701206
    24. S.D. Brown. Transfer of Multivariate Calibration Models. 2009, 345-378. https://doi.org/10.1016/B978-044452701-1.00077-6
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    27. Wei-Chuan Shih, Kate L. Bechtel, Michael S. Feld. Intrinsic Raman spectroscopy for quantitative biological spectroscopy Part I: Theory and simulations. Optics Express 2008, 16 (17) , 12726. https://doi.org/10.1364/OE.16.012726
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