6. Other issues

1. 6. Other issues Quimiometria Teórica e Aplicada Instituto de Química - UNICAMP

2. How many components to use? • Use ‘unfolding trick’ i.e. look at rank of each mode. • does not have strict statistical basis, but generally works well! • Use core-consistency diagnostic (PARAFAC). • also seems to work well in practice • Split-half analysis. • Does algorithm converge without problems? • Use full cross-validation. • N-way Toolbox now has a routine for this – can be slow! • Look at loadings and residuals. • Use chemical knowledge.

3. Mean-centering removes offsets from the data • removes constant background effects • can help to linearize data, i.e. Preprocessing: centering (1) • We are often interested in the differences between objects, not in their absolute values. • building calibration models: differences between samples

4. Three-way xjk X secondary variable object primary variable Preprocessing: centering (2) • When performing a calibration, it is most common to remove the mean value from each column: Two-way X object variable

5. Preprocessing: scaling (1) • Sometimes we want to analyse variables measured in different units • chemical engineering: temperatures, pressures, flow rates • QSAR: ionization constants, Hammett constants, dipole moments • These variables should be scaled in order to give variables an equal chance to appear in the model.

6. Three-way xjk X secondary variable object primary variable Autoscaling can destroy multilinear structure! Preprocessing: scaling (2) • For two-way arrays (object  variables), it is common to divide by the standard deviation after mean-centering the data (‘autoscaling’): Two-way X object variable

7. Double slab scaling may also be useful - ITERATIVE Xj Xk X process variable 2 object process variable 1 Preprocessing: scaling (3) Slab scaling maintains the multilinear structure! Xj X time object process variable

8. Tucker models • Tucker1: X = AG + E • Tucker1 = PCA • Tucker2: X = G(BA)T + E • G (I R2 R3) • very rarely used • Tucker3: X = AG(CB)T + E

9. time shift PARAFAC2 time shift object (I) time (K) wavelength (J) In PARAFAC2, only the matrix product XiXiT (JJ) is modelled. It works if the correlation structures in the objects are the same.

10. missing known • 1. Estimate model, (maximization) • 2. Replace missing values with model values • (expectation) Missing data • Expectation-maximization (EM) is a technique for estimating models (PARAFAC, Tucker, PLS, PCA etc.) when some of the data is missing: X = [X* X#] • 0. Initialize X# • 3. Repeat until convergence

11. Muito obrigado para sua atenção!