PARAFAC and Fluorescence

1. PARAFAC and Fluorescence Åsmund Rinnan Royal Veterinary and Agricultural University

2. Intro Fluorescence PARAFAC Fluor + PARAFAC Papers Challenges SOP MV Summary Intro – Fluorescence

3. Intro Fluorescence PARAFAC Fluor + PARAFAC Papers Challenges SOP MV Summary Intro – PARAFAC Can be seen as an expansion of PCA from two-way data to multi-way data X is the EEM a are the scores b are the emissionspectra c are the excitationspectra E is the residuals

4. Intro Fluorescence PARAFAC Fluor + PAR Papers Challenges SOP MV Summary Intro – Fluorescence Catechol Hydroquinone

5. Intro Fluorescence PARAFAC Fluor + PARAFAC Papers Challenges SOP MV Summary 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

6. Intro Fluorescence PARAFAC Fluor + PARAFAC Papers Challenges SOP MV Summary Intro – Challenges • Number of factors • Handling scatter effects • How to perform Second Order Prediction • Treating missing values in the EEM

7. Intro SOP Intro Alternatives Example MV Summary Second Order Prediction New samples Calibration set

8. Intro SOP Intro Alternatives Example MV Summary SOP – Introduction

9. Intro SOP Intro Alternatives Example MV Summary SOP – Alternatives C B = C A Calibration B New samples 0 A

10. Intro SOP Intro Alternatives Example Results Conclusion MV Summary 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

11. Intro SOP Intro Alternatives Example Results Conclusion MV Summary SOP – Ex: Results • Analyzed by ANOVA and PCA • Two very bad methods • Two good methods

12. Intro SOP Intro Alternatives Example Results Conclusion MV Summary SOP – Ex: Conclusion Best 2. best The 2 worst C Calibration B New samples 0 A A A

13. Intro SOP Intro Alternatives Example Results Conclusion MV Summary 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

14. Intro SOP MV Intro Discussion Alternatives Example Conclusion Summary 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

15. Intro SOP MV Intro Discussion Alternatives Example Conclusion Summary 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

16. Intro SOP MV Intro Discussion Alternatives Example Conclusion Summary MV – Alternatives Signal/ Data area Missing values Zeros

17. Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary MV – Example • 18 wood samples • 4 different levels of p-benzoquinone adsorbed in the fiber cell walls • 30 emission wavelengths x 35 excitation wavelengths

18. Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary MV – Ex: Results

19. Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary MV – Ex: Sample #1 None Weighted Zeros Non-Negativity

20. Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary MV – Ex: Excitation None Weighted Non-Negativity Zeros

21. Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary MV – Ex: Emission None Weighted Non-Negativity Zeros

22. Intro SOP MV Intro Discussion Alternatives Example Conclusion Summary MV – Conclusion • More interpretable results • # of iterations is less • Time before convergence is shorter

23. Intro SOP MV Summary Summary • Two of the challenges with PARAFAC and Fluorescence has been discussed • Just the beginning  A lot more work needs to be done

24. I would like to thank • Supervisor • Rasmus Bro • Second Order Prediction • Jordi Riu • Missing Values • Lisbeth G. Thygesen • Søren Barsberg • Jens K. S. Møller

25. Thank you for your attention www.models.kvl.dk