Eigenvector Research, Inc. Calibration Transfer ... · Before and After GLS 800 900 1000 1100 1200...
Transcript of Eigenvector Research, Inc. Calibration Transfer ... · Before and After GLS 800 900 1000 1100 1200...
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Generalized Least Squares forCalibration Transfer
Barry M. Wise, Harald Martens
and Martin Høy
Eigenvector Research, Inc.
Manson, WA
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Outline
• The calibration transfer problem• Instrument differences, drift, environment changes• Pseudo gasoline• Corn
• Generalized Least Squares preprocessing• PDS and OSC• Comparison of results• Conclusions
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Reasons for Calibration Transfer
• No two instruments identical• Some calibrations depend on very small changes in data
• Single instruments often drift• Aging parts, dirt
• Temperature
• Standardization
• New interferences in samples
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Pseudo Gasoline Data
benzenetoluenem-xylenep-xyleneoctane
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Difference Between Instruments
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Corn Data
MoistureOilProteinStarch
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Difference Between Instruments
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Selection of Transfer Samples
• Transfer samples should• be “high leverage”
• span the space of differences
• Several ways to choose• Hand select (based on PC scores, etc.)
• Find high leverage in PCA
• Find high leverage based on calibration model
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Development of GLS WeightingMatrix
Spec 1
Spec 2
MC Spec1
MC Spec 2
DifferenceDifferenceCovariance
InverseSqrt(Cov)
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Difference Covariance
Xd = (X1,tr − x 1,tr ) − (X2,tr − x 2,tr )
C =XdTXd
N −1
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Covariance to Weighting Matrix
C = VS2VT
G = VD−1VT
di,i−1 =
1si,i2
g2+1
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Effect of Parameter g
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Application of GLS WeightingMatrix
Spec 1Calibration
Data
GLS Weighting
Matrix
CalibrationModel
Spec 1New Data
Spec 2New Data
Mean Dif.
Predictions
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Piece-wise Direct Standardization
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PDS Model
X1 = X2F + 1b2−1
0
0F =
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Orthogonal Signal Correction
• Determine factor which describes large amountsof variance in X while being orthogonal to Y
• Deflate X
• Build PLS model that predicts scores of deflationfactor
• Use PLS model to estimate amount of factor toremove from new X
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Pseudo Gasoline Master Beforeand After GLS
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Wavelength (nm)
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Master Test Spectra Before Application of GLS
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Master Test Spectra After Application of GLS
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Pseudo Gasoline DifferenceBefore and After GLS
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Wavelength (nm)
Abso
rban
ceDifference Between Test Spectra Before Application of GLS
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Difference Between Test Spectra After Application of GLS
�movie
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Comparison of Methods on CornData
• Available data• 80 samples split 60/20• 3 instruments• 4 analytes
• 5 Transfer samples selected• Based on model inverse for PDS• Based on PCA leverage for OSC, GLS
• Tested all 3 methods on all combinations ofinstrument and analyte
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Issues with Meta-parameters
• GLS has only one parameter, g
• PDS• Window width
• Parameters for sub models (LVs or tolerance)
• OSC• Number of OSC LVs
• Tolerance of initial iterations
• Tolerance on reconstruction
• Number of LVs in PLS calibration models
• Try to shown each technique in best light!
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Typical Calibration and Test Data
3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 43
3.2
3.4
3.6
3.8
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3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 43
3.2
3.4
3.6
3.8
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Calibration Test
Calibration StandardizedTest Standardized
StandardizingMP5 to M5for Cornmoisture
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Results from Corn Data
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Results on Corn Data
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Comparison of Methods onPseudo Gasoline Data
• Available data• 30 samples split 20/10• 5 analytes• 2 instruments
• 5 Transfer samples selected• Based on model inverse for PDS• Based on PCA leverage for OSC, GLS
• Tested all 3 methods on all combinations ofinstrument and analyte
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Results on Pseudo Gasoline Data
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Other Ways to Apply GLS
• GLS weighting may be applied directly to model• Don’t have to rebuild model!
• Works well sometimes, but not always (future work)
• Downweight interferents• Requires estimate of effect of interferent
• Image decluttering
• Upweight analyte of interest
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Usability Issues
Yes
No
Yes
Affects netanalytesignal?
NoYesYesYes3OSC
YesNoNoNo2PDS
NoYesYes/NoNo1GLS
Transfer setsfunction ofY?
Modifiesspectra?
Rebuildcalibrationmodel?
Requires Y?Meta-parameters?
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Conclusions
• GLS preprocessing is a simple, effective methodfor eliminating spectral differences
• Can be used in several ways
• Only one adjustable parameter
• Potential loss of net analyte signal
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Bibliography
[1] H. Martens, M. Høy, B.M. Wise, R. Bro and P.B. Brockhoff, “GLS Preprocessing ofMultivariate Data,” submitted to J. Chemometrics, May 2001.
[2] Y. Wang, D.J. Veltkamp and B.R. Kowalski, “Multivariate InstrumentStandardization,” Anal. Chem., 63(23), pps 2750-2756, 1991.
[3] Z. Wang, T. Dean and B.R. Kowalski, “Additive Background Correction inMultivariate Instrument Standardization,” Anal. Chem., 67(14), pps 249-260, 1995.
[4] S. Wold, H. Antti, F. Lindgren and J. Öhman, “Orthogonal Signal Correction of Near-Infrared Spectra,” Chemo. and Intell. Lab. Sys., 44, pps 175-185, 1998.
[5] J. Sjöblom, O. Svensson, M. Josefson, H. Kullberg and S. Wold, “An Evaluation ofOrthogonal Signal Correction Applied to Calibration Transfer of Near Infrared Spectra,”Chemo. and Intell. Lab. Sys., 44, pps 229-244, 1998.
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Contact Information
Eigenvector Research, Inc.830 Wapato Lake RoadManson, WA 98831Phone: (509)687-2022Fax: (509)687-7033Email: [email protected]: eigenvector.com
This document may be downloaded fromhttp://www.eigenvector.com/Docs/GLS_Calibration_Trans.pdf