1. Threeway analysis Batch organic synthesis

2. 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

9. I J K A = batch B = variable C = time THREE-WAY ARRAY

10. 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.

11. Three-way arrays GC-MS LC-UV Fluorescence Batch processing many others

12. Properties Components / pseudorank 3 types, not 2 No orthogonality Parsimonious model

14. 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

15. REACTION

16. 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

19. 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

20. 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?

21. 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

32. 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

38. Batch # a1a1 block effect Fig 10.51

44. 0 0 1 2 3 4 5 6 Fig 10.55 12 3 4 5 Pseudorank Component size

50. Wavelength Bias

51. Wavelength Sum of squares

52. 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

53. Plotting Especially for 3-way analysis Paul Geladi

54. Plotting techniques Line / bar plots Box plots Quantile plots Autocorrelation plots Two-dimensional plots Three-dimensional plots Joint plots / biplots

55. Plotting techniques Response surfaces Imaging and mapping Movies Correlation spectroscopy Dendrograms Advanced interactive visualization in more dimensions

56. What do we want to do? Inspect raw data Detect outliers / groupings Select a model Build the model = calculate parameters Choose a pseudorank

57. What do we want to do? Inspect and use the model parameters Study the residuals Use the model for predictions More??

59. Properties Rectangular shape Every point exists Projection Resolution?

60. Properties Distances are correct Angles are meaningful

61. Topology Do all points have a continuum of close neighbours?

62. Wavenumber, cm -1 Absorbance Average NIR spectrum

63. What do we see? Data? Interpolation? Model? Are data fuzzy? Are models fuzzy?

64. The human eye is superb at detecting things But also very subjective

65. The remedies Background information Experience Objective techniques

66. Chemometrics is poisoned by (bad) line and scatter plots The biggest problem is with the scatter plots

67. Grain example FTNIR 10000-4000 cm -1 112 x 1501 Flour 5 Locations 10 Cultivars PCA after mean-centering

68. Line plot Horizontal: # comp. Vertical: singular value True Easiest

69. %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

70. t 2 (18%) t 3 (1.6%)

71. t 2 (18%) t 3 (1.6%)

72. Protein in flour PLS 6 components

73. Scatter plot requirements? Zero indicated? Orthonormal base? Equal scales? Mirroring?

74. PCA Never gives true spectra Never finds pure constituents Always rotates So why would scatter plots from it be useful?

75. Factor analysis is much better Factors are chemically meaningful Curve resolution PARAFAC

76. 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