PARAFAC and Fluorescence Åsmund Rinnan Royal Veterinary and Agricultural University

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

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

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

S econd O rder P rediction Calibration set New samples Intro SOP Intro Alternatives Example MV Summary

SOP – Introduction Intro SOP Intro Alternatives Example MV Summary

SOP – Alternatives = A B C Calibration New samples 0 A B C Intro SOP Intro Alternatives Example 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 Intro SOP Intro Alternatives Example Results Conclusion MV Summary

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

New samples SOP – Ex: Conclusion Calibration 0 A B C Best2. best A A The 2 worst 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 Intro SOP Intro Alternatives Example Results Conclusion MV Summary

M issing V alues – 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 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 Intro SOP MV Intro Discussion Alternatives Example Conclusion Summary

MV – Alternatives Missing values Zeros Signal/ Data area Intro SOP MV Intro Discussion Alternatives Example 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 Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary

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

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

MV – Ex: Excitation NoneWeighted Non-NegativityZeros Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary

MV – Ex: Emission Intro SOP MV Intro Discussion Alternatives Example Results EEM’s Conclusion Summary NoneWeighted Non-NegativityZeros

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

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

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