Definition and overview of chemometrics. Paul Geladi Head of Research NIRCE Chairperson NIR Nord Unit of Biomass Technology and Chemistry Swedish University.

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Presentation transcript:

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 btk.slu.se 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 = b 0 + b 1 x 1 + b 2 x b K x K + b 11 x b 22 x b KK x K 2 + b 12 x 1 x  Factors x 1, x 2,...x K 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

x y

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 SamplesSamples Vectors 1 K 1 I

A vector is a collection of numbers. It is always a column vector.

The transpose of a vector is a row vector. Symbols for transpose are ’ and T. a’ or a T

Particle size, 1 sample

Small particles, 35 samples

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

Size histograms, all samples Particle area

NIR wavelengths Times in batch reaction

Geometry of multivariate space

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

I patients 3 variables: blood oxygen, iron, hemoglobin

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

O2O2 Fe Hb

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 = [ x 1, x 2, x 3 ] || x || = ( x x x 3 2 ) 1/2

Geometry a b c c 2 = a 2 + b 2

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

Problem We can not see in more than 3 dimensions Paper, computer screen: dimensions

O2O2 Fe Hb

O2O2 Fe Hb

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