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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

800 900 1000 1100 1200 1300 1400 1500 1600-0.2

-0.1

0

0.1

Wavelength (nm)

Abso

rban

ce

Master Test Spectra Before Application of GLS

800 900 1000 1100 1200 1300 1400 1500 1600-0.2

-0.1

0

0.1

Wavelength (nm)

Abso

rban

ce

Master Test Spectra After Application of GLS

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Pseudo Gasoline DifferenceBefore and After GLS

800 900 1000 1100 1200 1300 1400 1500 1600-0.04

-0.02

0

0.02

Wavelength (nm)

Abso

rban

ceDifference Between Test Spectra Before Application of GLS

800 900 1000 1100 1200 1300 1400 1500 1600-0.04

-0.02

0

0.02

Wavelength (nm)

Abso

rban

ce

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

4

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: bmw@eigenvector.comWeb: eigenvector.com

This document may be downloaded fromhttp://www.eigenvector.com/Docs/GLS_Calibration_Trans.pdf