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Definition and overview of chemometrics

Definition and overview of chemometrics. Paul Geladi. Head of Research NIR CE 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. Project geography.

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Definition and overview of chemometrics

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  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

  3. Project geography

  4. Chemometrics Mathematics Statistics Computer Science In Chemistry

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

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

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

  8. Design of Experiments y = b0 + b1x1 + b2x2 +...+bKxK + b11x12 + b22x22 +...+ bKKxK2 + b12x1x2 +...+ e Factors x1, x2,...xK changed systematically Response y measured and modeled

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

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

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

  12. y x

  13. Multivariate Data Analysis

  14. Multivariate Data Analysis • Sampled data and design with too many reponses: • Mining • Hospitals • Agriculture • Food industry • More

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

  16. 34.92 Spectrum K 1 1 Samples Vectors I

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

  18. 12 3.6 11.1 5.9 34 0.5 1.4 17 The transpose of a vector is a row vector. Symbols for transpose are ’ and T. a’ or aT.

  19. Particle size, 1 sample

  20. Small particles, 35 samples

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

  22. Size histograms, all samples Particle area

  23. Times in batch reaction NIR wavelengths

  24. Geometry of multivariate space

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

  26. 3 variables: blood oxygen, iron, hemoglobin I patients

  27. Hb Fe O2

  28. Hb Fe O2

  29. Hb Fe O2

  30. Hb Fe O2

  31. Hb Fe O2

  32. Hb Fe O2

  33. Hb Fe O2

  34. Hb Fe O2

  35. Hb Fe O2

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

  37. 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

  38. Vectors (physics) x = [ x1, x2, x3 ] || x || = ( x12 + x22 + x32 ) 1/2

  39. Geometry c2 = a2 + b2 c a b

  40. Vectors (K dimensions) x = [ x1, x2,..., xK ] || x || = ( x12 + x22 +...+ xK2 ) 1/2

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

  42. Hb Fe O2

  43. Hb Fe O2

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

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