Net Analyte Signal Based Multivariate Calibration Methods

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4Th Iranian chemometrics Workshop (ICW)
Zanjan-2004
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The Problem of Factor Selection in
PCA-BasedCalibration Methods

• By
• Bahram Hemmateenejad
• Medicinal Natural Products Chemistry Research
  Center, Shiraz University of Medical Science

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Multivariate Calibration

• Regression Equation relating measurements on m
  samples to k different variables by
• y X b
• y (m?1) Dependent variable or Predicted
  Variable
• X (m?k) Independent variables or Predictor
  Variables
• b (k?1) regression coefficient

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• Multicomponent Analysis
• y concentration of the analyte
• X Recorded analytical signals at k different
  channels, i.e. absorbance at different wavelength

• QSAR/QSPR Studies
• y chemical property or biological activity
• X Molecular descriptors representing structural
  features of molecules by number

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Problems associated with MLR

• Colinearity between the independent variables (X)
• Number of dependent variables (k) should be much
  lower than the number of samples (m)

Reduced number of variables must be used
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• Feature selection
• The variables are selected based on their
  generalization ability using selection methods
  such as stepwise variable selection, genetic
  algorithm, simulated annealing,

• Feature extraction
• The variables are transformed into new
  coordinate axes with lower dimension
• Principal Component Analysis (PCA) or Factor
  Analysis (FA)

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PCA or FA or PFA

• X T P
• X (m?k)
• T (m?k)
• P (k?k)
• T t1 t2 t3 t4 t5 tk Score
• PTpT1 pT2 pT3 pT4 pT5 pTk Loading
• ? ?1 ?2 ?3 ?4 ?5 ?k eigen-value
• ?1 gt ?2 gt ?3 gt ?4 gt ?5 gt gt ?k

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• Each vector of T or P is named eigen-vector or
  PC or factor
• ?i shows the amount of variances in the X
  matrix that is explained by the corresponding
  eigen-vectors (ti or pi)

• A reduced set of PCs is necessary to reproduce
  the original data matrix without losing
  significant information

(m?k) (m?f) (f?k)
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• f is the number of significant factors
• f is the rank of the original data matrix
• f describes the complexity of the X matrix
• Ideally, f is the number of nonzero eigen-values
• f can be determined by the theory of FA
• Scree plot, indicator function, imbedded error,
  real error,

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PCA-Based regression method

• MLR (Classical Least Squares)
• y X b
• b (XTX)-1XTy
• ynew xnew b

• Principal Component Regression (PCR)
• X T P
• y T b
• b (TTT)-1TTy
• tnew xnew P
• ynew tnew b

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Some Questions

• How many PCs must be used in PCR?
• Which PCs should be considered in PCR modeling?
• Is the magnitude of an eigen-value necessarily a
  measure of its significance for the calibration?
• Significance of factor selection

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Top-down eigen-value ranking(ER)

• Factors are entered to the model based on their
  decreasing eigen-value one after the other
• Once new factor is entered, the regression model
  is build and its performances are validated by
  the existing procedures such as cross-validation

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Top-down Correlation Ranking (CR)

• First the correlation between each one of the
  factors and the dependent variable
  (concentration, y) is determined
• Then, the factors are entered to the models based
  on their decreasing correlation consecutively.

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Other factor selection methods

• Stepwise selection procedure
• Search algorithms
• Simulated annealing
• Genetic algorithm

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Some references

• Xie YL, Kalivas JH. Evaluation of principal
  component selection methods to form a global
  prediction model by principal component
  regression. Anal. Chim. Acta 1997 348 19-27.
• Sutter JM, Kalivas JH. Which principal components
  to utilize for principal component regression. J.
  Chemometrics 1992 6 217-225.
• Sun J. A correlation principal component
  regression analysis of NIR data. J. Chemometrics
  1995 9 21-29.
• Depczynski U, Frost VJ, Molt K. Genetic
  algorithms applied to the selection of factors in
  principal component regression. Anal. Chim. Acta
  2000 420 217-227.
• Barros AS, Rutledge DN. Genetic algorithm applied
  to the selection of principal components.
  Chemometrics Intell. Lab. Syst. 1998 40 65-81.
• Verdu-Andres J, Massart DL. Comparison of
  prediction-and correlation-Based methods to
  select the best Subset of principal components
  for principal component regression and detect
  outlying objects. Appl. Spect. 1998 52
  1425-1434.
• Xie YL, Kalivas JH. Local prediction models by
  principal component regression. Anal. Chim. Acta
  1997 348 29-38.
• Ferre L. Selection of components in principal
  component analysis a comparison of methods.
  Comput. Stat. Data Anal. 1995 19 669-682.

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A QSPR example

• Quantitative Structure-Electrochemistry
  Relationship Study of Some Organic Compounds
• Dependent variable
• Half-wave reduction potential (E1/2)of 69
  compounds
• Independent variables
• 1150 theoretical molecular descriptors calculated
  by DRAGON software

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Principal Component-Artificial Neural Network
(PC-ANN)

• ANN is a nonlinear non-parametric modeling method
• Feature selection is more important for ANN
• Feature selection-based ANN modeling is a complex
  procedure
• Orthogonalization of the variables before
  introducing to the network substantially
  decreases the computational time and increases
  the overall performances of the ANN
• PC-ANN is a feature extraction-based algorithm

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PC-GA-ANN Algorithm

• Genetic Algorithm Applied to the selection of
  Factors in PC-ANN modeling,
• The set of PCs selected by GA could model the
  structure-antagonist activity of the calcium
  channel blockers better than the ER procedure
• B. Hemmateenejad, M. Akhond, R. Miri, M.
  Shamsipur, J. Chem. Inf,. Comput. Sci. 43 (2003)
  1328.
• How are the factors ranked based on their
  correlation coefficient in PC-ANN?

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CR-PC-ANN Algorithm

• Correlation Ranking Procedure for factor
  selection in PC-ANN modeling,
• The nonlinear relationship between each one of
  the PCs and the dependent variable (y) was
  modeled by separate ANN models.
• It was found that the subset of PCs selected by
  CR was relatively the same as those selected by
  GA. Therefore the results of these factor
  selection procedures were similar
• B. Hemmateenejad, Chemometrics Intelligent
  Laboratory System, 2004, Accepted.

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• Application of ab initio theory to QSAR study of
  the 1,4-dihydrpyridine-based calcium channel
  blockers using GA-MLR and PC-GA-ANN procedures,
  B. Hemmateenejad, M.A. Safarpour, R.Miri, F.
  Taghavi, Journal of Computational Chemistry 25
  (2004) 1495.
• Highly Correlating Distance-Connectivity-Based
  Topological Indices. 2 Prediction of 15
  Properties of a Large Set of Alkanes Using a
  Stepwise Factor Selection-Based PCR Analysis, M.
  Shamsipur, R. Ghavami, B. Hemmateenejad, H.
  Sharghi, QSAR Combinatorial Sciences, 2004,
  Accepted.
• Quantitative Structure-Electrochemistry
  Relationship Study of some Organic Compounds
  using PCR and PC-ANN, B. Hemmateenejad, M.
  Shamsipur, Internet Electronic Journal of
  Molecular Design 3 (2004) 316.
• Toward an Optimal Procedure for PC-ANN Model
  Building Prediction of the Carcinogenic Activity
  of a Large Set of Drugs, B. Hemmateenejad, M.A.
  Safarpour, R. Miri, N. Nesari, Journal of
  Chemical Information and Computer Sciences,
  Revised
• Optimal QSAR analysis of the carcinogenic
  activity of drugs by correlation ranking and
  genetic algorithm-based PCR, B. Hemmateenejad,
  Journal of Chemometrics, Submitted.

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Feature Works

• Selection of Latent Variables in PLS
• Application of other selection algorithms such as
  successive projections algorithm
• Comparison between the importance of factor
  selection in multicomponent analysis and
  QSAR/QSPR studies
• Application of the factor selection-based ANN
  modeling in multicomponent analysis
• Validation of the different factor selection
  algorithms by new criteria