1. Definition and overview of chemometrics

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

5. Project geography

6. Chemometrics Mathematics Statistics Computer Science In Chemistry

7. Similar fields Biometrics ±1900 Psychometrics ±1930 Econometrics ±1950 Technometrics ±1960

8. Chemometrics Design of Experiments (DOE) Exploratory Data Analysis Classification Regression and Calibration

9. Design of Experiments Most important where possible Uses: ANOVA F-test t-test Plots Response Surfaces

10. Design of Experiments y = b 0 + b 1 x 1 + b 2 x 2 +...+b K x K + b 11 x 1 2 + b 22 x 2 2 +...+ b KK x K 2 + b 12 x 1 x 2 +...+  Factors x 1, x 2,...x K changed systematically Response y measured and modeled

11. Exploratory Data Analysis Design not possible Sampling situations Find structure Find groupings Find outliers

12. Classification Check for groupings = UNSUPERVISED Existing groupings = SUPERVISED Visualize groupings Classify Test

13. Regression / Calibration Two types of variables X / y Relationship linear / nonlinear Model Diagnostics Residual

14. x y

15. Multivariate Data Analysis

16. Sampled data and design with too many reponses: Mining Hospitals Agriculture Food industry More

17. Nomenclature Samples are objects What is measured on the object is a variable

18. 34.92 Spectrum SamplesSamples Vectors 1 K 1 I

19. 12 3.6 11.1 5.9 34 0.5 1.4 17 A vector is a collection of numbers. It is always a column vector.

20. The transpose of a vector is a row vector. Symbols for transpose are ’ and T. a’ or a T. 12 3.6 11.1 5.9 34 0.5 1.4 17

21. Particle size, 1 sample

22. Small particles, 35 samples

23. The Data Matrix A data matrix is a vector of vectors I K

24. Size histograms, all samples Particle area

25. NIR wavelengths Times in batch reaction

26. Geometry of multivariate space

27. Problem I and K can be large Correlation Univariate statistics does not apply

28. I patients 3 variables: blood oxygen, iron, hemoglobin

29. O2O2 Fe Hb

30. O2O2 Fe Hb

31. O2O2 Fe Hb

32. O2O2 Fe Hb

33. O2O2 Fe Hb

34. O2O2 Fe Hb

35. O2O2 Fe Hb

36. O2O2 Fe Hb

37. O2O2 Fe Hb

38. Properties of multivariate space Rotation vectors unchanged / distance unchanged Translation vectors changed / distance unchanged Rescaling / change units all changes

39. Consequences We can move the coordinate sytem around The relative distances between objects do not change We can rotate the coordinate system Scale changes are important Move coordinate system to center of data Scale properly

40. Vectors (physics) x = [ x 1, x 2, x 3 ] || x || = ( x 1 2 + x 2 2 + x 3 2 ) 1/2

41. Geometry a b c c 2 = a 2 + b 2

42. Vectors (K dimensions) x = [ x 1, x 2,..., x K ] || x || = ( x 1 2 + x 2 2 +...+ x K 2 ) 1/2

43. Problem We can not see in more than 3 dimensions Paper, computer screen: 2-2.5 dimensions

44. O2O2 Fe Hb

45. O2O2 Fe Hb

46. Projection 2D plane (screen, paper) Many projections possible Find a good one Find a few good ones What is good?