Definition and overview of chemometrics by UUU5Mu

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									Definition and overview of
      chemometrics
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
Project geography
Chemometrics


  Mathematics
    Statistics
Computer Science
  In Chemistry
              Similar fields

•   Biometrics ±1900
•   Psychometrics ±1930
•   Econometrics ±1950
•   Technometrics ±1960
             Chemometrics

•   Design of Experiments (DOE)
•   Exploratory Data Analysis
•   Classification
•   Regression and Calibration
         Design of Experiments
•   Most important where possible
•   Uses:
•   ANOVA
•   F-test
•   t-test
•   Plots
•   Response Surfaces
       Design of Experiments
y = b0 + b1x1 + b2x2 +...+bKxK + b11x12 +
b22x22 +...+ bKKxK2 + b12x1x2 +...+ e

Factors x1, x2,...xK changed systematically

Response y measured and modeled
    Exploratory Data Analysis

•   Design not possible
•   Sampling situations
•   Find structure
•   Find groupings
•   Find outliers
              Classification

•   Check for groupings = UNSUPERVISED
•   Existing groupings = SUPERVISED
•   Visualize groupings
•   Classify
•   Test
     Regression / Calibration
•   Two types of variables X / y
•   Relationship linear / nonlinear
•   Model
•   Diagnostics
•   Residual
y




    x
Multivariate Data Analysis
     Multivariate Data Analysis

•   Sampled data and design with too many reponses:
•   Mining
•   Hospitals
•   Agriculture
•   Food industry
•   More
                 Nomenclature




• Samples are objects
• What is measured on the object is a variable
34.92           Spectrum

        1 1                K
 S
 a
 m            Vectors
 p
 l
 e
 s
        I
       A vector is a collection
 12
       of numbers.
3.6
11.1
       It is always a column
5.9
       vector.
 34
0.5
1.4
 17
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.
Particle size, 1 sample
18


16


14


12


10


 8


 6


 4


 2


 0
     0   5   10   15   20   25
Small particles, 35 samples
  12




  10




   8




   6




   4




   2




   0
       0   5   10   15   20   25   30   35   40
    The Data Matrix
                         K


    A data matrix is a
    vector of vectors

I
Size histograms, all samples
  40


  35


  30


  25



  20


  15


  10


   5


   0
       0   5        10    15   20   25




               Particle area
Times in batch reaction
     4


    3.5


     3


    2.5



     2


    1.5


     1


    0.5


     0
          0   200   400   600   800   1000   1200




              NIR wavelengths
Geometry of multivariate space
            Problem


       I and K can be large
            Correlation
Univariate statistics does not apply
3 variables: blood oxygen,
iron, hemoglobin

I patients
     Hb




          Fe

O2
     Hb




          Fe

O2
     Hb




          Fe

O2
     Hb




          Fe

O2
     Hb




          Fe

O2
     Hb




          Fe

O2
     Hb



          Fe


O2
     Hb




          Fe
O2
     Hb




          Fe

O2
Properties of multivariate space
                Rotation
 vectors unchanged / distance unchanged
               Translation
  vectors changed / distance unchanged
         Rescaling / change units
               all changes
            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
       Vectors (physics)


     x = [ x1, x2, x3 ]

|| x || = ( x12 + x22 + x32 ) 1/2
            Geometry


                 c2 = a2 + b2
a       c


    b
  Vectors (K dimensions)


     x = [ x1, x2,..., xK ]

|| x || = ( x12 + x22 +...+ xK2 ) 1/2
             Problem


We can not see in more than 3 dimensions

Paper, computer screen: 2-2.5 dimensions
     Hb




          Fe

O2
     Hb




          Fe

O2
   Projection

2D plane (screen, paper)
Many projections possible
   Find a good one
 Find a few good ones


   What is good?

								
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