Introduction to Chemometrics

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Introduction to Chemometrics

• Sergey Kucheryavskiy
• ACABS research group
• Aalborg University, campus Esbjerg
• www.acabs.dk

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What is Chemometrics?

• WikipediaChemometrics is the application of
  mathematical or statistical methods to chemical
  data
• International Chemometrics SocietyChemometrics
  is the science of relating measurements made on a
  chemical system or process to the state of the
  system via application of mathematical or
  statistical methods
• D. L. MassartChemometrics is the chemical
  discipline that uses mathematical, statistical
  and other methods employing formal logic to
  design or select optimal measurement procedures
  and experiments, and to provide maximum relevant
  chemical information by analyzing chemical data

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What is Chemometrics?

• B.M. Mariyanov, Lectures on Chemometrics, Tomsk
  State University
• Quality control in chemical analysis
• Mathematical modeling
• Processing of analyte signals
• Pattern recognition
• Databases. Artificial intelligence
• Application of Information Theory in Chemistry

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What is Chemometrics?

• A.V. Garmash, Introduction to Chemometrics and
  Chemical Metrology, Moscow State University
• Mathematical statistics basics
• Normal distribution
• Variance analysis
• Variance analysis in Chemistry
• Correlation analysis
• Classification and identification. Pattern
  recognition
• Regression and calibration
• Design of experiments

Chemometrics Statistics? Chemometrics
Statistics in Analytical Chemistry?
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What is Chemometrics?

• Chemometrics is a data analytical discipline,
  such as
• Deals with multivariate (and multiway) data
• Based on soft modeling
• Uses projection methods and concept of latent
  variables
• Considers data as information noise
• Considers noise as useless information

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Multivariate data
Variables
Samples
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Multivariate and multiway data
Many inputs induce an effect Many effects are
derived from one input etc
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Many variables and many samples
One measurement spectrum (600 points)
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Soft and hard modeling
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Projection methods and latent variables
Data without structure
Data with hidden structure
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Projection methods and latent variables
Formal dimension number of variables Effective
dimension number of latent variables that cover
all data variance
Formal dimension 3
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Projection methods and latent variables
Formal dimension number of variables Effective
dimension number of latent variables that cover
all data variance
Effective dimension 1
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Projection methods and latent variables

• Projection to latent variable subspace
• allows to reduce dimension
• provides possibility for visual data analysis

How to find latent variables?
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Principal component space

• Choose latent variable (first principal
  component, PC1) along direction of maximum
  variance
• Project all samples to PC1
• Residual variance
• considered as noise (useless information)
• modeled by PC2

PC1
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Principal component space
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Principal component analysis
Loadings
Scores
Raw data
Residuals
Data
Model
Noise
X
TPT
E
TPT


Explained variance
Residual variance
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PCA Scores
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PCA Scores
T

• Row sample PC coordinates
• Column projection of samples to PC

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PCA Loadings
PT

• Row PC basis vector in variable space
• Column projection of variable basis vector to
  PC space

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??????? ???????? E
. . . . .

• ei distance from sample to PC space
• e2tot residual variance

ei
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Example 1 Wine analysis
Three types of Italian wine grown in the same
region but fermented from three different
cultivars (grapes) 178 samples x 13 variables
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Example 1 Wine analysis
Scores and Loadings plots PCA main tools
Scores
Loadings
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Example 2 AMT analysis of coated pellets
1
2
3
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AMT-spectra
PCA scores
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PCA conclusions

• Principal Component Analysis
• Works with X data measurements, observations,
  etc.
• Chooses latent variables (Principal Components)
  along maximum variance directions
• Scores and Loadings plots are the main PCA tools
• Principal components are orthogonal!

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Multivariate calibration
Spectra
Concentrations
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Example 3 polyaromatic hydrocarbons
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Example 3 polyaromatic hydrocarbons
Simulated spectra
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Example 3 polyaromatic hydrocarbons
MLR-regression
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Projection on Latent Structure

• Both X and Y data modelled jointly
• Two sets of scores (T, U) and loadings (P, Q)
  plus loading-weights (W) are calculated
• Calculations are iterative, aim to maximaze
  Covariance(T, U)
• Prediction Y Tnew Bt Y Xnew B B
  W(PTW)-1QT

X TPT Ex Y UQT Ey
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Example 3 polyaromatic hydrocarbons
PLS-regression
C1
C2
C3
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Example 3 polyaromatic hydrocarbons
PLS
MLR
C1
C3
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Example 4 estimation of octane number
K. Esbensen. Multivariate Data Analysis in
Practice. Camo, 2002
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Example 4 estimation of octane number
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What Chemometrics can do?
Tasks
Methods
PCA
Dimension reduction Analysis of data structure
Discrimination and classification
PCA, SIMCA
Multivariate calibration
PCR, PLS
Prediction
and much more!
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What Chemometrics can do?
Multivariate Curve Resolution
Multivariate Image Analysis
MSPC/PAT
Nonlinear regression
Multivay analysis
Design of Experiments
Chemometrics
Linear algebra
Statistics
Sampling
Matlab
Excel
Instruments