PARAFAC and Fluorescence

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PARAFAC and Fluorescence

• Åsmund Rinnan
• Royal Veterinary and Agricultural University

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

• 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
  RQCompetitive 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

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

• Number of factors
• Handling scatter effects

• How to perform Second Order Prediction
• Treating missing values in the EEM

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Second Order Prediction
Intro SOP Intro Alternatives
Example MV Summary
Calibration set
New samples
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SOP Introduction
Intro SOP Intro Alternatives
Example MV Summary
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SOP Alternatives
Intro SOP Intro Alternatives
Example MV Summary
C
B

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

• 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

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SOP Ex Results
Intro SOP Intro Alternatives Example
Results Conclusion MV Summary

• Analyzed by ANOVA and PCA
• Two very bad methods
• Two good methods

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

• 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

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Missing Values Intro
Intro SOP MV Intro Discussion Alternatives
Example Conclusion Summary

• Can be treated with
• Letting PARAFAC handle the missing values
• Weighting the missing area down
• Non-negativity constraints
• Insertion of 0s into the matrix

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MV Discussion
Intro SOP MV Intro Discussion Alternatives
Example Conclusion Summary

• In theory it is wrong to insert 0s
• 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

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MV Alternatives
Intro SOP MV Intro Discussion Alternatives
Example Conclusion Summary
Signal/ Data area
Missing values
Zeros
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MV Example
Intro SOP MV Intro Discussion Alternatives
Example Results EEMs
Conclusion Summary

• 18 wood samples
• 4 different levels of p-benzoquinone adsorbed in
  the fiber cell walls
• 30 emission wavelengths x 35 excitation
  wavelengths

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MV Ex Results
Intro SOP MV Intro Discussion Alternatives
Example Results EEMs
Conclusion Summary
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MV Ex Sample 1
Intro SOP MV Intro Discussion Alternatives
Example Results EEMs
Conclusion Summary
None
Weighted
Zeros
Non-Negativity
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MV Ex Excitation
Intro SOP MV Intro Discussion Alternatives
Example Results EEMs
Conclusion Summary
None
Weighted
Non-Negativity
Zeros
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MV Ex Emission
Intro SOP MV Intro Discussion Alternatives
Example Results EEMs
Conclusion Summary
None
Weighted
Non-Negativity
Zeros
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MV Conclusion
Intro SOP MV Intro Discussion Alternatives
Example Conclusion Summary

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

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Summary
Intro SOP MV Summary

• Two of the challenges with PARAFAC and
  Fluorescence has been discussed
• Just the beginning ? A lot more work needs to be
  done

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I would like to thank

• Supervisor
• Rasmus Bro
• Second Order Prediction
• Jordi Riu
• Missing Values
• Lisbeth G. Thygesen
• Søren Barsberg
• Jens K. S. Møller

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Thank you for your attention

• www.models.kvl.dk