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Threeway analysis Batch organic synthesis
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Paul Geladi Head of Research NIRCE Chairperson NIR Nord Unit of Biomass Technology and Chemistry Swedish University of Agricultural Sciences Umeå Technobothnia Vasa paul.geladi @ btk.slu.se paul.geladi @ syh.fi
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I J K A = batch B = variable C = time THREE-WAY ARRAY
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Literature Geladi P. & Åberg P., Three-way modeling of a batch organic synthesis process monitored by near infrared spectroscopy, Journal of Near Infrared Spectroscopy, 9, 1-9, 2001 Geladi P. & Forsström J., Monitoring of a batch organic synthesis by infrared spectroscopy: modeling and interpretation of three-way data, Journal of Chemometrics, 16, 329-338, 2002.
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Three-way arrays GC-MS LC-UV Fluorescence Batch processing many others
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Properties Components / pseudorank 3 types, not 2 No orthogonality Parsimonious model
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BATCH REACTION ester synthesis by refluxing alcohol and acid many batches as experimental design measure NIR spectrum with transflectance fiberoptic probe at regular intervals 400-2500 nm every 2 nm, 32 scans average reference = air
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REACTION
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C 5 H 11 OH + CH 3 COOH -> C 5 H 11 OCOCH 3 + H 2 O -acid catalysis H + -remove water to shift equilibrium
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Parsimony = not using too many model parameters = no overfitting 10 Stations x 13 Variables x 22 Times 2 Components MODELPARAMETERS PCA1 10x28620 + 572 = 592 PCA2 13x22026 + 440 = 466 PCA3 22x13044 + 260 = 304 PARAFAC20 + 26 + 44 = 92
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IMPORTANT QUESTIONS - can we learn something about reaction kinetics? - can we see difference between batches? - can we interpret the spectra? - how does it all fit together?
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REACTION 1 14 x 701 x 13 array. Source of SS% explained Rank 3 model 97.1 Residual 2.9 Total 100 Component 1 48.0 Component 2 15.3 Component 3 4.0
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REACTION 2 6 x 40 x 776 array number%SSSS 1622.73 2180.78 3160.71 43.20.14 Model99.24.38 Residual0.80.038 Total1004.42
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Batch # a1a1 block effect Fig 10.51
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0 0 1 2 3 4 5 6 Fig 10.55 12 3 4 5 Pseudorank Component size
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Wavelength Bias
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Wavelength Sum of squares
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CONCLUSIONS It is possible: rank 3-4 Preprocessing needed (derivative) Interpretation of time (reaction kinetics) Interpretation of batch mode (design) Interpretation of spectral mode needs pure standards What is the mystery chemical? Visual interpretation as line or loading plots
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Plotting Especially for 3-way analysis Paul Geladi
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Plotting techniques Line / bar plots Box plots Quantile plots Autocorrelation plots Two-dimensional plots Three-dimensional plots Joint plots / biplots
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Plotting techniques Response surfaces Imaging and mapping Movies Correlation spectroscopy Dendrograms Advanced interactive visualization in more dimensions
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What do we want to do? Inspect raw data Detect outliers / groupings Select a model Build the model = calculate parameters Choose a pseudorank
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What do we want to do? Inspect and use the model parameters Study the residuals Use the model for predictions More??
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Properties Rectangular shape Every point exists Projection Resolution?
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Properties Distances are correct Angles are meaningful
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Topology Do all points have a continuum of close neighbours?
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Wavenumber, cm -1 Absorbance Average NIR spectrum
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What do we see? Data? Interpolation? Model? Are data fuzzy? Are models fuzzy?
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The human eye is superb at detecting things But also very subjective
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The remedies Background information Experience Objective techniques
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Chemometrics is poisoned by (bad) line and scatter plots The biggest problem is with the scatter plots
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Grain example FTNIR 10000-4000 cm -1 112 x 1501 Flour 5 Locations 10 Cultivars PCA after mean-centering
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Line plot Horizontal: # comp. Vertical: singular value True Easiest
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%SS explained based on eigenvalues # %SS Cumulative 1 78.89 78.89 2 18.21 97.10 3 1.56 98.66 4 0.77 99.43 5 0.11 99.54 6 0.08 99.62 7 0.06 99.68
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t 2 (18%) t 3 (1.6%)
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t 2 (18%) t 3 (1.6%)
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Protein in flour PLS 6 components
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Scatter plot requirements? Zero indicated? Orthonormal base? Equal scales? Mirroring?
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PCA Never gives true spectra Never finds pure constituents Always rotates So why would scatter plots from it be useful?
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Factor analysis is much better Factors are chemically meaningful Curve resolution PARAFAC
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Making PARAFAC loadings look good X = A ( C B )’ + E ^ = X + E X = USV’ + E US is the space of A in the orthonormal basis of V
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