PARAFAC and Fluorescence

Åsmund RinnanRoyal Veterinary and Agricultural

University

Intro – Fluorescence

Intro Fluorescence PARAFAC Fluor + PARAFAC Papers ChallengesSOPMVSummary

Intro – PARAFAC

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X is the EEMa are the scoresb are the emissionspectrac are the excitationspectraE is the residuals

Can be seen as an expansion of PCA from two-way data to multi-way data

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Intro Fluorescence PARAFAC Fluor + PARAFAC Papers ChallengesSOPMVSummary

Intro – Fluorescence

Catechol

Hydroquinone

Intro Fluorescence PARAFAC Fluor + PAR Papers ChallengesSOPMVSummary

Intro – Papers• Christensen J, Povlsen VT, Sorensen J: Application of fluorescence spectroscopy

and chemometrics in the evaluation of processed cheese during storage, Journal of Dairy Science, 86 (4), 2003, 1101-1107

• Xie HP, Chu X, Jiang JH, Cui H, Shen GL, Yu RQ:Competitive interactions of adriamycin and ethidium bromide with DNA as studied by full rank parallel factor analysis of fluorescence three-way array data, Spectrochimica Acta Part A – Molecular and Biomolecular Spectroscopy, 59 (4), 2003, 743-749

• da Silva JCGE, Leitao JMM, Costa FS, Ribeiro JLA: Detection of verapamil drug by fluorescence and trilinear decompositim techniques, Analytica Chimica Acta, 453 (1), 2002, 105-115

• Marcos A, Foulkes M, Hill SJ: Application of a multi-way method to study long-term stability in ICP-AES, Journal of Analytical Atomic Spectrometry, 16 (2), 2001, 105-114

• JiJi RD, Andersson GG, Booksh KS: Application of PARAFAC for calibration with excitation-emission matrix fluorescence spectra of three classes of environmental pollutants, Journal of Chemometrics, 14 (3), 2000, 171-185

Intro Fluorescence PARAFAC Fluor + PARAFAC Papers ChallengesSOPMVSummary

Intro – Challenges

• Number of factors• Handling scatter effects

• How to perform Second Order Prediction

• Treating missing values in the EEM

Intro Fluorescence PARAFAC Fluor + PARAFAC Papers ChallengesSOPMVSummary

Second Order PredictionC

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IntroSOP Intro Alternatives ExampleMVSummary

SOP – Introduction

IntroSOP Intro Alternatives ExampleMVSummary

SOP – Alternatives

=A

B

C

Calibration

New samples 0A

B

C

IntroSOP Intro Alternatives ExampleMVSummary

SOP – Example

• All simulated data• 3 or 4 analytes in calibration set• 3 interferents• Different kind of overlap between analytes

and interferents• Four different noise levels• 7, 4, 3 and 2 samples in the calibration set• One or several samples in the test set• 10 different noise additions 10

replicates

IntroSOP Intro Alternatives Example Results ConclusionMVSummary

SOP – Ex: Results

• Analyzed by ANOVA and PCA

• Two very bad methods

• Two good methods

IntroSOP Intro Alternatives Example Results ConclusionMVSummary

New samples

SOP – Ex: Conclusion

Calibration

0A

B

CBest2. best

A

A

The 2 worst

IntroSOP Intro Alternatives Example Results ConclusionMVSummary

SOP – Ex: Conclusion

• Fixing B and C gives the best result• However, deciding the number of

factors is tricky with only one sample• First use 2. best method to evaluate

the number of factors, then fix B and C and compute with the right number of components

IntroSOP Intro Alternatives Example Results ConclusionMVSummary

Missing Values – Intro

Can be treated with:• Letting PARAFAC

handle the missing values

• Weighting the missing area down

• Non-negativity constraints

• Insertion of 0’s into the matrix

IntroSOPMV Intro Discussion Alternatives Example ConclusionSummary

MV – Discussion

• In theory it is wrong to insert 0’s• The actual values are not known

Missing values should be used• However, the values should

theoretically be close to zero • Inserting zeros would force PARAFAC

to a specific number almost like a constraint

• It seems to work in practice

IntroSOPMV Intro Discussion Alternatives Example ConclusionSummary

MV – Alternatives

Missingvalues

Zeros

Signal/ Data area

IntroSOPMV Intro Discussion Alternatives Example ConclusionSummary

MV – Example

• 18 wood samples• 4 different levels of p-benzoquinone

adsorbed in the fiber cell walls• 30 emission wavelengths x 35 excitation

wavelengths

IntroSOPMV Intro Discussion Alternatives Example Results EEM’s ConclusionSummary

MV – Ex: Results

IntroSOPMV Intro Discussion Alternatives Example Results EEM’s ConclusionSummary

MV – Ex: Sample #1

IntroSOPMV Intro Discussion Alternatives Example Results EEM’s ConclusionSummary

None Weighted

Non-Negativity Zeros

MV – Ex: ExcitationN

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Non

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Zero

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IntroSOPMV Intro Discussion Alternatives Example Results EEM’s ConclusionSummary

MV – Ex: Emission

IntroSOPMV Intro Discussion Alternatives Example Results EEM’s ConclusionSummary

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MV – Conclusion

• More interpretable results• # of iterations is less• Time before convergence is shorter

IntroSOPMV Intro Discussion Alternatives Example ConclusionSummary

Summary

• Two of the challenges with PARAFAC and Fluorescence has been discussed

• Just the beginning A lot more work needs to be done

IntroSOPMVSummary

I would like to thank

• Supervisor– Rasmus Bro

• Second Order Prediction– Jordi Riu

• Missing Values– Lisbeth G. Thygesen– Søren Barsberg– Jens K. S. Møller

Thank you for your attention

www.models.kvl.dk